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Relevant bibliographies by topics / General theory for finite groups

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Journal articles

Academic literature on the topic 'General theory for finite groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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Journal articles on the topic "General theory for finite groups"

1

Hansen, Vagn Lundsgaard, and Peter Petersen. "Groups, Coverings and Galois Theory." Canadian Journal of Mathematics 43, no. 6 (1991): 1281–93. http://dx.doi.org/10.4153/cjm-1991-073-0.

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AbstractFinite extensions of complex commutative Banach algebras are naturally related to corresponding finite covering maps between the carrier spaces for the algebras. In the case of function rings, the finite extensions are induced by the corresponding finite covering maps, and the topological properties of the coverings are strongly reflected in the algebraic properties of the extensions and conversely. Of particular interest to us is the class of finite covering maps for which the induced extensions of function rings admit primitive generators. This is exactly the class of polynomial covering maps and the extensions are algebraic extensions defined by the underlying Weierstrass polynomials.The purpose of this paper is to develop a suitable Galois theory for finite extensions of function rings induced by finite covering maps and to apply it in the case of Weierstrass polynomials and polynomial covering maps.

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2

Hanaki, Akihide, Masahiko Miyamoto, and Daisuke Tambara. "Quantum Galois theory for finite groups." Duke Mathematical Journal 97, no. 3 (1999): 541–44. http://dx.doi.org/10.1215/s0012-7094-99-09720-x.

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3

Levi, Ran. "On finite groups and homotopy theory." Memoirs of the American Mathematical Society 118, no. 567 (1996): 0. http://dx.doi.org/10.1090/memo/0567.

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4

Goyal, Pallav. "Invariant theory of finite general linear groups modulo Frobenius powers." Communications in Algebra 46, no. 10 (2018): 4511–29. http://dx.doi.org/10.1080/00927872.2018.1448842.

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5

Meierfrankenfeld, U., G. Parmeggiani, and B. Stellmacher. "Baumann-components of finite groups of characteristic p, general theory." Journal of Algebra 515 (December 2018): 19–51. http://dx.doi.org/10.1016/j.jalgebra.2018.08.014.

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6

Hall, J. I. "The general theory of 3-transposition groups." Mathematical Proceedings of the Cambridge Philosophical Society 114, no. 2 (1993): 269–94. http://dx.doi.org/10.1017/s0305004100071589.

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A set D of 3-transpositions in the group G is a normal set of elements of order 2 such that, for all d and e in D, the order of the product de is 1, 2, or 3. If G is generated by the conjugacy class D of 3-transpositions, we say that (G, D) is a 3-transposition group or (loosely) that G is a 3-transposition group. The study of 3-transposition groups was instituted by Bernd Fischer [6, 7, 8] who classified all 3-transposition groups which are finite and have no non-trivial normal solvable subgroups. Recently the present author and H. Cuypers[5] extended Fischer's result to include all 3-transposition groups with trivial centre. For this classification the present paper provides the extension of Fischer's paper [8] where he gave two basic reductions, the Normal Subgroup Theorem and the Transitivity Theorem stated below. Other results of help in the classification are also presented here.

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7

Lubotzky, Alexander, and Avinoam Mann. "Residually finite groups of finite rank." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 3 (1989): 385–88. http://dx.doi.org/10.1017/s0305004100068110.

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The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters’, show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird. Thus it seems reasonable to impose the type of condition that enables us to apply the theory of finite groups. Two such conditions are local finiteness and residual finiteness, and here we are interested in the latter. Specifically, we consider residually finite groups of finite rank, where a group is said to have rank r, if all finitely generated subgroups of it can be generated by r elements. Recall that a group is said to be virtually of some property, if it has a subgroup of finite index with this property. We prove the following result:Theorem 1. A residually finite group of finite rank is virtually locally soluble.

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8

Isaacs, I. M. "Book Review: Character theory of finite groups." Bulletin of the American Mathematical Society 36, no. 04 (1999): 489–93. http://dx.doi.org/10.1090/s0273-0979-99-00789-2.

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9

Holt, Derek F. "Book Review: Theory of finite simple groups." Bulletin of the American Mathematical Society 46, no. 1 (2008): 151–56. http://dx.doi.org/10.1090/s0273-0979-08-01215-9.

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10

Bruner, R. R., та J. P. C. Greenlees. "The connective 𝐾-theory of finite groups". Memoirs of the American Mathematical Society 165, № 785 (2003): 0. http://dx.doi.org/10.1090/memo/0785.

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