Relevant bibliographies by topics / Polycyclic groups][Algebraic groups

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Polycyclic groups][Algebraic groups'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Polycyclic groups][Algebraic groups"

1

Sautoy, Marcus Du. "Polycyclic Groups, Analytic Groups and Algebraic Groups." Proceedings of the London Mathematical Society 85, no. 1 (2002): 62–92. http://dx.doi.org/10.1112/plms/85.1.62.

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MEYEROVITCH, TOM. "Pseudo-orbit tracing and algebraic actions of countable amenable groups." Ergodic Theory and Dynamical Systems 39, no. 9 (2018): 2570–91. http://dx.doi.org/10.1017/etds.2017.126.

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Consider a countable amenable group acting by homeomorphisms on a compact metrizable space. Chung and Li asked if expansiveness and positive entropy of the action imply existence of an off-diagonal asymptotic pair. For algebraic actions of polycyclic-by-finite groups, Chung and Li proved that they do. We provide examples showing that Chung and Li’s result is near-optimal in the sense that the conclusion fails for some non-algebraic action generated by a single homeomorphism, and for some algebraic actions of non-finitely generated abelian groups. On the other hand, we prove that every expansiv
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LICHTMAN, A. I. "RESTRICTED LIE ALGEBRAS OF POLYCYCLIC GROUPS." Journal of Algebra and Its Applications 05, no. 05 (2006): 571–627. http://dx.doi.org/10.1142/s0219498806001892.

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We consider some classes of polycyclic groups which have a p-series such that the restricted graded Lie algebra associated to this p-series is free abelian. We also study p-series and restricted Lie algebras associated to them in arbitrary polycyclic groups.
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Assmann, Björn, and Bettina Eick. "Computing polycyclic presentations for polycyclic rational matrix groups." Journal of Symbolic Computation 40, no. 6 (2005): 1269–84. http://dx.doi.org/10.1016/j.jsc.2005.05.003.

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Sinanan, S. K., and D. F. Holt. "Algorithms for polycyclic-by-finite groups." Journal of Symbolic Computation 79 (March 2017): 269–84. http://dx.doi.org/10.1016/j.jsc.2016.02.008.

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Nikolaev, Andrey, and Alexander Ushakov. "Subset sum problem in polycyclic groups." Journal of Symbolic Computation 84 (January 2018): 84–94. http://dx.doi.org/10.1016/j.jsc.2017.03.007.

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Franciosi, Silvana, Francesco Giovanni, and Martin L. Newell. "Groups with Polycyclic Non-Normal Subgroups." Algebra Colloquium 7, no. 1 (2000): 33–42. http://dx.doi.org/10.1007/s10011-000-0033-1.

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Ostheimer, Gretchen. "Practical Algorithms for Polycyclic Matrix Groups." Journal of Symbolic Computation 28, no. 3 (1999): 361–79. http://dx.doi.org/10.1006/jsco.1999.0287.

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Asri, M. S. M., K. B. Wong, and P. C. Wong. "Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups." Algebra Colloquium 28, no. 01 (2021): 119–30. http://dx.doi.org/10.1142/s1005386721000110.

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We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form [Formula: see text], where [Formula: see text] has infinite order and [Formula: see text] is finite.
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Garreta, Albert, Alexei Miasnikov, and Denis Ovchinnikov. "Diophantine problems in solvable groups." Bulletin of Mathematical Sciences 10, no. 01 (2020): 2050005. http://dx.doi.org/10.1142/s1664360720500058.

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We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions. For each group [Formula: see text] in one of these classes, we prove that there exists a ring of algebraic integers [Formula: see text] that is interpretable in [Formula: see text] by finite systems of equations ([Formula: see text]-interpretable), and hence that the Diophantine problem in [Formula: see text] is polynomial time reducible to th
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Dissertations / Theses on the topic "Polycyclic groups][Algebraic groups"

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Du, Sautoy M. P. F. "Discrete groups, analytic groups and Poincare series." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236109.

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Assmann, Björn. "Applications of Lie methods to computations with polycyclic groups." Thesis, St Andrews, 2007. http://hdl.handle.net/10023/435.

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Silva, Jefferson dos Santos e. "Uma apresentação policíclica para o multiplicador de Schur e o quadrado tensorial não abeliano de um grupo policíclico." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4539.

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Submitted by Erika Demachki (erikademachki@gmail.com) on 2015-05-18T18:27:17Z No. of bitstreams: 2 Dissertação - Jefferson dos Santos e Silva - 2015.pdf: 741852 bytes, checksum: 8cb431ec9a186100784d60268a133fcf (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2015-05-18T18:28:34Z (GMT) No. of bitstreams: 2 Dissertação - Jefferson dos Santos e Silva - 2015.pdf: 741852 bytes, checksum: 8cb431ec9a186100784d60268a133fcf (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a77147
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Garibaldi, Skip. "Trialitarian algebraic groups /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9906492.

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Meyer, Aurel Nathan. "Essential dimension of algebraic groups." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/27091.

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We study the essential dimension of linear algebraic groups. For a group G, essential dimension is a measure for the complexity of G-torsors or, more generally, the complexity of any algebraic or geometric structure with automorphism group G. This makes essential dimension a powerful invariant with many interesting and surprising connections to problems in algebra and geometry. We show that for various classes of groups, including finite (algebraic) groups and algebraic tori, the essential dimension is related to minimal faithful representations. In many cases this renders the exact value of t
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Brundan, Jonathan Walter. "Double cosets in algebraic groups." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244137.

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Craven, David Andrew. "Algebraic modules for finite groups." Thesis, University of Oxford, 2007. http://ora.ox.ac.uk/objects/uuid:7f641b33-d301-4445-8269-a5a33f4b7e5e.

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The main focus of this thesis is algebraic modules---modules that satisfy a polynomial equation with integer co-efficients in the Green ring---in various finite groups, as well as their general theory. In particular, we ask the question `when are all the simple modules for a finite group G algebraic?' We call this the (p-)SMA property. The first chapter introduces the topic and deals with preliminary results, together with the trivial first results. The second chapter provides the general theory of algebraic modules, with particular attention to the relationship between algebraic modules and t
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Clarke, Matthew Charles. "Unipotent elements in algebraic groups." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/241660.

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This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements in the Lie algebra g = LieG. The first topic is a determination of canonical forms for unipotent classes and nilpotent orbits of G. Using an original approach, we begin by obtaining a new canonical form for nilpotent matrices, up to similarity, which is symmetric with respect to the non-main diagonal (i.e. it is fixed by the map f : (xi;j) -> (xn+1-j;n+1-i)), with entries in
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Dos, Santos João Pedro Pinto. "Fundamental groups in algebraic geometry." Thesis, University of Cambridge, 2006. https://www.repository.cam.ac.uk/handle/1810/252015.

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Sinanan, Shavak. "Algorithms for polycyclic-by-finite groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/49186/.

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A set of fundamental algorithms for computing with polycyclic-by-finite groups is presented here. Polycyclic-by-finite groups arise naturally in a number of contexts; for example, as automorphism groups of large finite soluble groups, as quotients of finitely presented groups, and as extensions of modules by groups. No existing mode of representation is suitable for these groups, since they will typically not have a convenient faithful permutation representation. A mixed mode is used to represent elements of such a group; utilising a polycyclic presentation or a power-conjugate presentation fo
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Books on the topic "Polycyclic groups][Algebraic groups"

1

Group and ring theoretic properties of polycyclic groups. Springer, 2009.

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Tschinkel, Yuri, ed. Algebraic groups. Göttingen University Press, 2007. http://dx.doi.org/10.17875/gup2007-57.

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Onishchik, Arkadij L. Lie Groups and Algebraic Groups. Springer Berlin Heidelberg, 1990.

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B, Vinberg Ė. Lie groups and algebraic groups. Springer Verlag, 1990.

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Onishchik, Arkadij L., and Ernest B. Vinberg. Lie Groups and Algebraic Groups. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-74334-4.

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Ariki, Susumu, Hiraku Nakajima, Yoshihisa Saito, Ken-ichi Shinoda, Toshiaki Shoji, and Toshiyuki Tanisaki, eds. Algebraic Groups and Quantum Groups. American Mathematical Society, 2012. http://dx.doi.org/10.1090/conm/565.

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Linear algebraic groups. 2nd ed. Birkhäuser, 2009.

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Borel, Armand. Linear algebraic groups. 2nd ed. Springer-Verlag, 1991.

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Differential algebraic groups. Academic Press, 1985.

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Humphreys, James E. Linear algebraic groups. 5th ed. Springer, 1998.

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Book chapters on the topic "Polycyclic groups][Algebraic groups"

1

Lawson, Mark V. "The Polycyclic Inverse Monoids and the Thompson Groups Revisited." In Semigroups, Categories, and Partial Algebras. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4842-4_12.

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Onishchik, Arkadij L., and Ernest B. Vinberg. "Algebraic Varieties." In Lie Groups and Algebraic Groups. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-74334-4_2.

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Onishchik, Arkadij L., and Ernest B. Vinberg. "Algebraic Groups." In Lie Groups and Algebraic Groups. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-74334-4_3.

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Taylor, Joseph. "Algebraic groups." In Graduate Studies in Mathematics. American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/046/15.

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Seitz, G. M. "Algebraic Groups." In Finite and Locally Finite Groups. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_2.

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Bahturin, Yuri. "Algebraic Groups." In Basic Structures of Modern Algebra. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0839-5_7.

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Harris, Joe. "Algebraic Groups." In Algebraic Geometry. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2189-8_10.

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Droste, Manfred, and Rüdiger Göbel. "The Automorphism Groups of Hahn Groups." In Ordered Algebraic Structures. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5640-0_8.

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Wallach, Nolan R. "Lie Groups and Algebraic Groups." In Universitext. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65907-7_2.

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Goodman, Roe, and Nolan R. Wallach. "Lie Groups and Algebraic Groups." In Graduate Texts in Mathematics. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-79852-3_1.

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Conference papers on the topic "Polycyclic groups][Algebraic groups"

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MALGRANGE, B. "DIFFERENTIAL ALGEBRAIC GROUPS." In Algebraic Approach to Differential Equations. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814273244_0007.

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Wang, Lifang, and Yanming Wang. "On CN–Groups and CT–Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0051.

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KERZ, MORITZ. "ON NEGATIVE ALGEBRAIC K-GROUPS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0049.

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Nebe, Gabriele. "Computing with Arithmetic Groups." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. ACM, 2017. http://dx.doi.org/10.1145/3087604.3087661.

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Golasiński, Marek, Daciberg L. Gonçalves, and Peter N. Wong. "A note on generalized equivariant homotopy groups." In Algebraic Topology - Old and New. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc85-0-12.

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DVUREČENSKIJ, ANATOLIJ. "ON THE ROLE OF ℓ-GROUPS AND PO-GROUPS FOR ALGEBRAIC AND QUANTUM STRUCTURES". У Proceedings of the QL&SC 2012. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814401531_0002.

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Sharygin, G. I. "A new construction of characteristic classes for noncommutative algebraic principal bundles." In Noncommutative Geometry and Quantum Groups. Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-15.

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Bialostocki, A., and T. Shaska. "Galois groups of prime degree polynomials with nonreal roots." In Computational Aspects of Algebraic Curves. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701640_0015.

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Xu, Chuanyu. "New Properties of Algebraic Structure of Vague Groups." In 2007 IEEE International Conference on Control and Automation. IEEE, 2007. http://dx.doi.org/10.1109/icca.2007.4376487.

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Symonds, Peter. "On the construction of permutation complexes for profinite groups." In School and Conference in Algebraic Topology. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.11.369.

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