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

Research output: Contribution to journalArticle

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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 languageEnglish
Pages (from-to)1273-1280
Number of pages8
JournalInternational Journal of Algebra and Computation
Volume15
Issue number5-6
DOIs
Publication statusPublished - 1 Oct 2005

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Linear Group
Galois field
Subgroup
K-group
Intersection

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Conjugately dense subgroups of 3-dimensional linear groups over locally finite field. / Zyubin, S. A.

In: International Journal of Algebra and Computation, Vol. 15, No. 5-6, 01.10.2005, p. 1273-1280.

Research output: Contribution to journalArticle

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