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Relevant bibliographies by topics / Finite index subgroups

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Academic literature on the topic 'Finite index subgroups'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Finite index subgroups"

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Srinivasan, S. "Maximal subgroups of finite groups." International Journal of Mathematics and Mathematical Sciences 13, no. 2 (1990): 311–14. http://dx.doi.org/10.1155/s016117129000045x.

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In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting subgroup of the group.

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Kappe, Luise-Charlotte. "Finite coverings by 2-engel groups." Bulletin of the Australian Mathematical Society 38, no. 1 (August 1988): 141–50. http://dx.doi.org/10.1017/s0004972700027350.

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Bear's characterisation of central-by-finite groups as groups possessing a finite covering by abelian subgroups if the starting point for this invertigation. We characterise groups with a finite covering by 2-Engel subgroups as groups for which the subgroup of right 2-Engel elements has finite index; and the groups having a finite covering by normal 2-Engel subgroups are exactly the 3-Engel groups among those having a finite covering by 2-Engel subgroups. The second centre of a group having a finite covering by class two subgroups does not necessarily have finite index. However, a group has a finite covering by subgroups in a variety containing all cyclic groups if the margin of thes variety in the group has finite index.

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De Falco, M., F. De Giovanni, C. Musella, and Y. P. Sysak. "The structure of groups whose subgroups are permutable-by-finite." Journal of the Australian Mathematical Society 81, no. 1 (August 2006): 35–48. http://dx.doi.org/10.1017/s1446788700014622.

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AbstractA subgroup H of a group G is said to be permutable if HX = XH for each subgroup X of G, and the group G is called quasihamiltonian if all its subgroups are permutable. We shall say that G is a Q F-group if every subgroup H of G contains a subgroup K of finite index which is permutable in G. It is proved that every locally finite Q F-group contains a quasihamiltonian subgroup of finite index. In the proof of this result we use a theorem by Buckley, Lennox, Neumann, Smith and Wiegold concerning the corresponding problem when permutable subgroups are replaced by normal subgroups: if G is a locally finite group such that H/HG is finite for every subgroup H, then G contains an abelian subgroup of finite index.

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DE GIOVANNI, F., M. MARTUSCIELLO, and C. RAINONE. "LOCALLY FINITE GROUPS WHOSE SUBGROUPS HAVE FINITE NORMAL OSCILLATION." Bulletin of the Australian Mathematical Society 89, no. 3 (November 20, 2013): 479–87. http://dx.doi.org/10.1017/s000497271300097x.

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AbstractIf $X$ is a subgroup of a group $G$, the cardinal number $\min \{ \vert X: X_{G}\vert , \vert {X}^{G} : X\vert \} $ is called the normal oscillation of $X$ in $G$. It is proved that if all subgroups of a locally finite group $G$ have finite normal oscillation, then $G$ contains a nilpotent subgroup of finite index.

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Nikolov, Nikolay, and Dan Segal. "Finite index subgroups in profinite groups." Comptes Rendus Mathematique 337, no. 5 (September 2003): 303–8. http://dx.doi.org/10.1016/s1631-073x(03)00349-2.

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M�ller, Thomas. "Counting free subgroups of finite index." Archiv der Mathematik 59, no. 6 (December 1992): 525–33. http://dx.doi.org/10.1007/bf01194843.

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Haglund, Frédéric. "Finite index subgroups of graph products." Geometriae Dedicata 135, no. 1 (May 27, 2008): 167–209. http://dx.doi.org/10.1007/s10711-008-9270-0.

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NIKOLAEV, ANDREY V., and DENIS E. SERBIN. "FINITE INDEX SUBGROUPS OF FULLY RESIDUALLY FREE GROUPS." International Journal of Algebra and Computation 21, no. 04 (June 2011): 651–73. http://dx.doi.org/10.1142/s0218196711006388.

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Using graph-theoretic techniques for f.g. subgroups of Fℤ[t] we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. As an application we obtain an analogue of Greenberg–Stallings Theorem for f.g. fully residually free groups, and prove that a f.g. nonabelian subgroup of a f.g. fully residually free group is of finite index in its normalizer and commensurator.

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Szepietowski, Błażej. "On finite index subgroups of the mapping class group of a nonorientable surface." Glasnik Matematicki 49, no. 2 (December 18, 2014): 337–50. http://dx.doi.org/10.3336/gm.49.2.08.

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HARTUNG, RENÉ. "COSET ENUMERATION FOR CERTAIN INFINITELY PRESENTED GROUPS." International Journal of Algebra and Computation 21, no. 08 (December 2011): 1369–80. http://dx.doi.org/10.1142/s0218196711006637.

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We describe an algorithm that computes the index of a finitely generated subgroup in a finitely L-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely L-presented group is decidable. As an application, we consider the low-index subgroups of some self-similar groups including the Grigorchuk group, the twisted twin of the Grigorchuk group, the Grigorchuk super-group, and the Hanoi 3-group.

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Dissertations / Theses on the topic "Finite index subgroups"

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Wall, Liam. "Homology in Finite Index Subgroups." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526420.

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Firth, David. "An algorithm to find normal subgroups of a finitely presented group, up to a given finite index." Thesis, University of Warwick, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.417029.

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Krämer, Stefan [Verfasser]. "Numerical calculation of automorphic functions for finite index subgroups of triangle groups / Stefan Krämer." Bonn : Universitäts- und Landesbibliothek Bonn, 2015. http://d-nb.info/1079273379/34.

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Zeron-Medina, Mariano. "Residual deficiency as a gradient, deficiency in finite index subgroups, p-deficiency and largeness." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608052.

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Momeni, Arash [Verfasser]. "Induced representations of the modular group PSL(2,Z) and the transfer operator for its subgroups of finite index / Arash Momeni." Clausthal-Zellerfeld : Universitätsbibliothek Clausthal, 2014. http://d-nb.info/1057895903/34.

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Nuez, González Javier de la [Verfasser], and Katrin [Akademischer Betreuer] Tent. "On expansions of non-abelian free groups by cosets of a finite index subgroup / Javier de la Nuez González ; Betreuer: Katrin Tent." Münster : Universitäts- und Landesbibliothek Münster, 2016. http://d-nb.info/114190764X/34.

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Hartung, René. "Computation with finitely L-presented groups." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F065-7.

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Books on the topic "Finite index subgroups"

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Farb, Benson, and Dan Margalit. Moduli Space. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0013.

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This chapter focuses on the moduli space of Riemann surfaces. The moduli space parameterizes many different kinds of structures on Sɡ, such as isometry classes of hyperbolic structures on S, conformal classes of Riemannian metrics on S, biholomorphism classes of complex structures on S, and isomorphism classes of smooth algebraic curves homeomorphic to S. The chapter first considers the moduli space as the quotient of Teichmüller space before discussing the moduli space of the torus. It then examines the theorem (due to Fricke) that Mod(S) acts properly discontinuously on Teich(S), with a finite-index subgroup of Mod(S) acting freely such that M(S) is finitely covered by a smooth aspherical manifold. The chapter also looks at Mumford's compactness criterion, which describes what it means to go to infinity in M(S), and concludes by showing that M(Sɡ) is very close to being a classifying space for Sɡ-bundles.

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Farb, Benson, and Dan Margalit. The Symplectic Representation and the Torelli Group. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0007.

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This chapter discusses the basic properties and applications of a symplectic representation, denoted by Ψ‎, and its kernel, called the Torelli group. After describing the algebraic intersection number as a symplectic form, the chapter presents three different proofs of the surjectivity of Ψ‎, each illustrating a different theme. It also illustrates the usefulness of the symplectic representation by two applications to understanding the algebraic structure of Mod(S). First, the chapter explains how this representation is used by Serre to prove the theorem that Mod(Sɡ) has a torsion-free subgroup of finite index. It thens uses the symplectic representation to prove, following Ivanov, the following theorem of Grossman: Mod(Sɡ) is residually finite. It also considers some of the pioneering work of Dennis Johnson on the Torelli group. In particular, a Johnson homomorphism is constructed and some of its applications are given.

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Book chapters on the topic "Finite index subgroups"

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Lee, Gregory T., and Sudarshan K. Sehgal. "Generators of Subgroups of Finite Index in GL m (ℤG)." In Advances in Ring Theory, 211–19. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1978-1_17.

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Clay, Matt. "Free Groups and Folding." In Office Hours with a Geometric Group Theorist. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691158662.003.0004.

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This chapter studies subgroups of free groups using the combinatorics of graphs and a simple operation called folding. It introduces a topological model for free groups and uses this model to show the rank of the free group H and whether every finitely generated nontrivial normal subgroup of a free group has finite index. The edge paths and the fundamental group of a graph are discussed, along with subgroups via graphs. The chapter also considers five applications of folding: the Nielsen–Schreier Subgroup theorem, the membership problem, index, normality, and residual finiteness. A group G is residually finite if for every nontrivial element g of G there is a normal subgroup N of finite index in G so that g is not in N. Exercises and research projects are included.

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Kondrat’ev, Anatoly S., Natalia Maslova, and Danila Revin. "On the Pronormality of Subgroups of Odd Index in Finite Simple Groups." In Groups St Andrews 2017 in Birmingham, 406–18. Cambridge University Press, 2019. http://dx.doi.org/10.1017/9781108692397.016.

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"Appendix A. Torsion-Free Subgroups of Finite Index by Hans-Christoph Im Hof." In Complex Ball Quotients and Line Arrangements in the Projective Plane, 189–96. Princeton: Princeton University Press, 2016. http://dx.doi.org/10.1515/9781400881253-010.

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Conference papers on the topic "Finite index subgroups"

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KURTH, CHRIS A., and LING LONG. "COMPUTATIONS WITH FINITE INDEX SUBGROUPS OF PSL2(ℤ) USING FAREY SYMBOLS." In Proceedings of the Second International Congress in Algebra and Combinatorics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790019_0015.

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