Conjugately dense subgroups of 3-dimensional linear groups over locally finite field

Abstract

A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL ₃(K) ≤ G ≤ GL₃(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL₃(K) over locally finite field K.

Original language	English
Pages (from-to)	1273-1280
Number of pages	8
Journal	International Journal of Algebra and Computation
Volume	15
Issue number	5-6
DOIs	https://doi.org/10.1142/S0218196705002608
Publication status	Published - 1 Oct 2005

Keywords

Conjugacy class
Irreducible and conjugately dense subgroup
Special and general linear group

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1142/S0218196705002608

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title = "Conjugately dense subgroups of 3-dimensional linear groups over locally finite field",

abstract = "A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in {"}Kourovka Notebook{"} for the group GL3(K) over locally finite field K.",

keywords = "Conjugacy class, Irreducible and conjugately dense subgroup, Special and general linear group",

author = "Zyubin, {S. A.}",

year = "2005",

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language = "English",

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AU - Zyubin, S. A.

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N2 - A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL3(K) over locally finite field K.

AB - A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL3(K) over locally finite field K.

KW - Conjugacy class

KW - Irreducible and conjugately dense subgroup

KW - Special and general linear group

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