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Relevant bibliographies by topics / Permutation groups. Finite groups

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Academic literature on the topic 'Permutation groups. Finite groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Permutation groups. Finite groups"

1

Burns, J. M., B. Goldsmith, B. Hartley, and R. Sandling. "On quasi-permutation representations of finite groups." Glasgow Mathematical Journal 36, no. 3 (September 1994): 301–8. http://dx.doi.org/10.1017/s0017089500030901.

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In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent to which some facts about permutation groups generalize to the quasi-permutation group situation. Here we investigate further the analogy between permutation groups and quasipermutation groups by studying the relation between the minimal degree of a faithful permutation representation of a given finite group G and the minimal degree of a faithful quasi-permutation representation. We shall often prefer to work over the rational field rather than the complex field.

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Banica, Teodor, Julien Bichon, and Sonia Natale. "Finite quantum groups and quantum permutation groups." Advances in Mathematics 229, no. 6 (April 2012): 3320–38. http://dx.doi.org/10.1016/j.aim.2012.02.012.

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Vesanen, Ari. "Finite classical groups and multiplication groups of loops." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 3 (May 1995): 425–29. http://dx.doi.org/10.1017/s0305004100073278.

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Let Q be a loop; then the left and right translations La(x) = ax and Ra(x) = xa are permutations of Q. The permutation group M(Q) = 〈La, Ra | a ε Q〉 is called the multiplication group of Q; it is well known that the structure of M(Q) reflects strongly the structure of Q (cf. [1] and [8], for example). It is thus an interesting question, which groups can be represented as multiplication groups of loops. In particular, it seems important to classify the finite simple groups that are multiplication groups of loops. In [3] it was proved that the alternating groups An are multiplication groups of loops, whenever n ≥ 6; in this paper we consider the finite classical groups and prove the following theorems

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., Haci Aktas. "On Finite Topological Permutation Groups." Journal of Applied Sciences 2, no. 1 (December 15, 2001): 60–61. http://dx.doi.org/10.3923/jas.2002.60.61.

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Lucchini, Andrea. "Enumerating Transitive Finite Permutation Groups." Bulletin of the London Mathematical Society 30, no. 6 (November 1998): 569–77. http://dx.doi.org/10.1112/s0024609398004846.

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HOARE, A. H. M. "SUBGROUPS OF N.E.C. GROUPS AND FINITE PERMUTATION GROUPS." Quarterly Journal of Mathematics 41, no. 1 (1990): 45–59. http://dx.doi.org/10.1093/qmath/41.1.45.

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Niemenmaa, Markku. "Decomposition of Transformation Groups of Permutation Machines." Fundamenta Informaticae 10, no. 4 (October 1, 1987): 363–67. http://dx.doi.org/10.3233/fi-1987-10403.

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By a permutation machine we mean a triple (Q,S,F), where Q and S are finite sets and F is a function Q × S → Q which defines a permutation on Q for every element from S. These permutations generate a permutation group G and by considering the structure of G we can obtain efficient ways to decompose the transformation group (Q,G). In this paper we first consider the situation where G is half-transitive and after this we show how to use our result in the general non-transitive case.

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NEUMANN, PETER M., CHERYL E. PRAEGER, and SIMON M. SMITH. "SOME INFINITE PERMUTATION GROUPS AND RELATED FINITE LINEAR GROUPS." Journal of the Australian Mathematical Society 102, no. 1 (October 25, 2016): 136–49. http://dx.doi.org/10.1017/s1446788716000343.

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This article began as a study of the structure of infinite permutation groups $G$ in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy min-n, the minimal condition on normal subgroups. The groups $G$ are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal nontrivial normal subgroups, or they have a regular normal subgroup $M$ which is a divisible abelian $p$-group of finite rank. In the latter case the point stabilisers are finite and act irreducibly on a $p$-adic vector space associated with $M$. This leads to our second variation, which is a study of the finite linear groups that can arise.

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Praeger, Cheryl E., and Aner Shalev. "Bounds on finite quasiprimitive permutation groups." Journal of the Australian Mathematical Society 71, no. 2 (October 2001): 243–58. http://dx.doi.org/10.1017/s1446788700002895.

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AbstractA permutation group is said to be quasiprimitive if every nontrivial normal subgroup is transitive. Every primitive permutation group is quasiprimitive, but the converse is not true. In this paper we start a project whose goal is to check which of the classical results on finite primitive permutation groups also holds for quasiprimitive ones (possibly with some modifications). The main topics addressed here are bounds on order, minimum degree and base size, as well as groups containing special p-elements. We also pose some problems for further research.

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Pearson, Mike, and Ian Short. "Magic letter groups." Mathematical Gazette 91, no. 522 (November 2007): 493–99. http://dx.doi.org/10.1017/s0025557200182130.

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Certain numeric puzzles, known as ‘magic letters’, each have a finite permutation group associated with them in a natural manner. We describe how the isomorphism type of these permutation groups relates to the structure of the magic letters.

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Dissertations / Theses on the topic "Permutation groups. Finite groups"

1

Walton, Jacqueline. "Representing the quotient groups of a finite permutation group." Thesis, University of Warwick, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340088.

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Xu, Jing. "On closures of finite permutation groups /." Connect to this title, 2005. http://theses.library.uwa.edu.au/adt-WU2006.0023.

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Xu, Jing. "On closures of finite permutation groups." University of Western Australia. School of Mathematics and Statistics, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0023.

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[Formulae and special characters in this field can only be approximated. See PDF version for accurate reproduction] In this thesis we investigate the properties of k-closures of certain finite permutation groups. Given a permutation group G on a finite set Ω, for k ≥ 1, the k-closure G(k) of G is the largest subgroup of Sym(Ω) with the same orbits as G on the set Ωk of k-tuples from Ω. The first problem in this thesis is to study the 3-closures of affine permutation groups. In 1992, Praeger and Saxl showed if G is a finite primitive group and k ≥ 2 then either G(k) and G have the same socle or (G(k),G) is known. In the case where the socle of G is an elementary abelian group, so that G is a primitive group of affine transformations of a finite vector space, the fact that G(k) has the same socle as G gives little information about the relative sizes of the two groups G and G(k). In this thesis we use Aschbacher’s Theorem for subgroups of finite general linear groups to show that, if G ≤ AGL(d, p) is an affine permutation group which is not 3-transitive, then for any point α ∈ Ω, Gα and (G(3) ∩ AGL(d, p))α lie in the same Aschbacher class. Our results rely on a detailed analysis of the 2-closures of subgroups of general linear groups acting on non-zero vectors and are independent of the finite simple group classification. In addition, modifying the work of Praeger and Saxl in [47], we are able to give an explicit list of affine primitive permutation groups G for which G(3) is not affine. The second research problem is to give a partial positive answer to the so-called Polycirculant Conjecture, which states that every transitive 2-closed permutation group contains a semiregular element, that is, a permutation whose cycles all have the same length. This would imply that every vertex-transitive graph has a semiregular automorphism. In this thesis we make substantial progress on the Polycirculant Conjecture by proving that every vertex-transitive, locally-quasiprimitive graph has a semiregular automorphism. The main ingredient of the proof is the determination of all biquasiprimitive permutation groups with no semiregular elements. Publications arising from this thesis are [17, 54].

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Benjamin, Ian Francis. "Quasi-permutation representations of finite groups." Thesis, University of Liverpool, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250561.

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Vauhkonen, Antti Kalervo. "Finite primitive permutation groups of rank 4." Thesis, Imperial College London, 1993. http://hdl.handle.net/10044/1/58543.

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In this thesis we classify finite primitive permutation groups of rank 4. According to the 0' Nan-Scott theorem, a finite primitive permutation group is an affine group, an almost simple group, or has either simple diagonal action, product action or twisted wreath action. In Chapter 1 we completely determine the primitive rank 4 permutation groups with one of the last three types of actions up to permutation equivalence. In Chapter 2 we use Aschbacher's subgroup structure theorem for the finite classical groups to reduce the classification of affine primitive rank 4 permutation groups G of degree p*^ (p prime) to the case where a point stabilizer G in G satisfies soc(G/Z(G ))=L for some ^ 0 0 0 non-abelian simple group L. In Chapter 3 we classify all such groups G with L a simple group of Lie type over a finite field of characteristic p. Finally, in Chapter 4 we determine all the faithful primitive rank 4 permutation representations of the finite linear groups up to permutation equivalence.

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Torres, Bisquertt María de la Luz. "Symmetric generation of finite groups." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2625.

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Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

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Bamblett, Jane Carswell. "Algorithms for computing in finite groups." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240616.

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Kasouha, Abeir Mikhail. "Symmetric representations of elements of finite groups." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2605.

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This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

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Menezes, Nina E. "Random generation and chief length of finite groups." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3578.

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Part I of this thesis studies P[subscript(G)](d), the probability of generating a nonabelian simple group G with d randomly chosen elements, and extends this idea to consider the conditional probability P[subscript(G,Soc(G))](d), the probability of generating an almost simple group G by d randomly chosen elements, given that they project onto a generating set of G/Soc(G). In particular we show that for a 2-generated almost simple group, P[subscript(G,Soc(G))](2) 53≥90, with equality if and only if G = A₆ or S₆. Furthermore P[subscript(G,Soc(G))](2) 9≥10 except for 30 almost simple groups G, and we specify this list and provide exact values for P[subscript(G,Soc(G))](2) in these cases. We conclude Part I by showing that for all almost simple groups P[subscript(G,Soc(G))](3)≥139/150. In Part II we consider a related notion. Given a probability ε, we wish to determine d[superscript(ε)] (G), the number of random elements needed to generate a finite group G with failure probabilty at most ε. A generalisation of a result of Lubotzky bounds d[superscript(ε)](G) in terms of l(G), the chief length of G, and d(G), the minimal number of generators needed to generate G. We obtain bounds on the chief length of permutation groups in terms of the degree n, and bounds on the chief length of completely reducible matrix groups in terms of the dimension and field size. Combining these with existing bounds on d(G), we obtain bounds on d[superscript(ε)] (G) for permutation groups and completely reducible matrix groups.

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Lemieux, Stephane R. "Minimal degree of faithful permutation representations of finite groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0015/MQ48492.pdf.

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Books on the topic "Permutation groups. Finite groups"

1

Behravesh, Houshang. Quasi-permutation representations of finite groups. Manchester: University of Manchester, 1995.

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Walton, Jacqueline. Representing the quotient groups of a finite permutation group. [s.l.]: typescript, 1999.

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3

Liebeck, M. W. Regular subgroups of primitive permutation groups. Providence, R.I: American Mathematical Society, 2010.

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1948-, Praeger Cheryl E., and Saxl J. (Jan) 1948-, eds. Regular subgroups of primitive permutation groups. Providence, R.I: American Mathematical Society, 2010.

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Character theory of finite groups: Conference in honor of I. Martin Isaacs, June 3-5, 2009, Universitat de Valencia, Valencia, Spain. Providence, R.I: American Mathematical Society, 2010.

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Brian, Mortimer, ed. Permutation groups. New York: Springer, 1996.

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Cameron, Peter J. Permutation groups. Cambridge: Cambridge University Press, 1999.

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Passman, Donald S. Permutation groups. Mineola, N.Y: Dover Publications, Inc., 2012.

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Dixon, John D., and Brian Mortimer. Permutation Groups. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0731-3.

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Cameron, Peter J. Oligomorphic permutation groups. Cambridge: Cambridge University Press, 1990.

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Book chapters on the topic "Permutation groups. Finite groups"

1

Kurzweil, Hans, and Bernd Stellmacher. "Permutation Groups." In The Theory of Finite Groups, 77–97. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21768-1_4.

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Saxl, J. "Finite Simple Groups and Permutation Groups." In Finite and Locally Finite Groups, 97–110. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_4.

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Robinson, Derek J. S. "Finite Permutation Groups." In A Course in the Theory of Groups, 185–205. New York, NY: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4684-0128-8_7.

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Robinson, Derek J. S. "Finite Permutation Groups." In A Course in the Theory of Groups, 192–212. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4419-8594-1_7.

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Steinberg, Benjamin. "Group Actions and Permutation Representations." In Representation Theory of Finite Groups, 83–96. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0776-8_7.

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Praeger, Cheryl E. "Finite primitive permutation groups: A survey." In Lecture Notes in Mathematics, 63–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0100731.

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Macpherson, Dugald. "Permutation Groups Whose Subgroups Have Just Finitely Many Orbits." In Ordered Groups and Infinite Permutation Groups, 221–29. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-3443-9_8.

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Hiss, Gerhard, and Frank Lübeck. "Some Remarks on Two-Transitive Permutation Groups as Multiplication Groups of Quasigroups." In Buildings, Finite Geometries and Groups, 81–91. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0709-6_5.

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Praeger, Cheryl E., Cai Heng Li, and Alice C. Niemeyer. "Finite transitive permutation groups and finite vertex-transitive graphs." In Graph Symmetry, 277–318. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8937-6_7.

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Kornyak, Vladimir V. "Splitting Permutation Representations of Finite Groups by Polynomial Algebra Methods." In Developments in Language Theory, 304–18. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99639-4_21.

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Conference papers on the topic "Permutation groups. Finite groups"

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Smith, Robert, and Brendan Pawlowski. "Efficient Finite Permutation Groups and Homomesy Computation in Common Lisp." In ILC '14: 2014 International Lisp Conference. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2635648.2635664.

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Babai, L., E. Luks, and A. Seress. "Permutation groups in NC." In the nineteenth annual ACM conference. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/28395.28439.

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Babai, L., E. M. Luks, and A. Seress. "Fast management of permutation groups." In [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science. IEEE, 1988. http://dx.doi.org/10.1109/sfcs.1988.21943.

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Banica, Teodor, Julien Bichon, and Benoît Collins. "Quantum permutation groups: a survey." In Noncommutative Harmonic Analysis with Applications to Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc78-0-1.

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Kabanov, Vladislav, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Graphs and Transitive Permutation Groups." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498638.

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Luks, Eugene M., Ferenc Rákóczi, and Charles R. B. Wright. "Computing normalizers in permutation p-groups." In the international symposium. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/190347.190390.

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Egner, Sebastian, and Markus Püschel. "Solving puzzles related to permutation groups." In the 1998 international symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/281508.281611.

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Fiat, A., S. Moses, A. Shamir, I. Shimshoni, and G. Tardos. "Planning and learning in permutation groups." In 30th Annual Symposium on Foundations of Computer Science. IEEE, 1989. http://dx.doi.org/10.1109/sfcs.1989.63490.

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Luks, Eugene M., and Pierre Mckenzie. "Fast parallel computation with permutation groups." In 26th Annual Symposium on Foundations of Computer Science (sfcs 1985). IEEE, 1985. http://dx.doi.org/10.1109/sfcs.1985.26.

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PRAEGER, CHERYL E. "REGULAR PERMUTATION GROUPS AND CAYLEY GRAPHS." In Proceedings of the 13th General Meeting. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277686_0003.

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Reports on the topic "Permutation groups. Finite groups"

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Holmes, Richard B. Signal Processing on Finite Groups. Fort Belvoir, VA: Defense Technical Information Center, February 1990. http://dx.doi.org/10.21236/ada221129.

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Elkholy, Abd-Elmoneim Mohamed, Mohamed Hussein Hafez Abd-ellatif, and Sarah Hassan El-sherif. Influence of S-permutable GS-subgroups on Finite Groups. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, July 2019. http://dx.doi.org/10.7546/crabs.2019.07.01.

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Zhai, Liangliang, and Xuanlong Ma. Perfect Codes in Proper Order Divisor Graphs of Finite Groups. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, December 2020. http://dx.doi.org/10.7546/crabs.2020.12.04.

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Moradipour, Kayvan. Conjugacy Class Sizes and n-th Commutativity Degrees of Some Finite Groups. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, May 2018. http://dx.doi.org/10.7546/crabs.2018.04.02.

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