Conjugately dense subgroups of locally finite Chevalley groups of Lie rank 1

Abstract

Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.

Original language	English
Pages (from-to)	581-586
Number of pages	6
Journal	Siberian Mathematical Journal
Volume	44
Issue number	4
DOIs	https://doi.org/10.1023/A:1024772104335
Publication status	Published - 1 Jul 2003

Keywords

Chevalley group
Conjugately dense subgroup
Locally finite field
Monomial subgroup
Parabolic subgroup

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1023/A:1024772104335

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title = "Conjugately dense subgroups of locally finite Chevalley groups of Lie rank 1",

abstract = "Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.",

keywords = "Chevalley group, Conjugately dense subgroup, Locally finite field, Monomial subgroup, Parabolic subgroup",

author = "Zyubin, {S. A.} and Levchuk, {V. M.}",

year = "2003",

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day = "1",

doi = "10.1023/A:1024772104335",

language = "English",

volume = "44",

pages = "581--586",

journal = "Siberian Mathematical Journal",

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AU - Zyubin, S. A.

AU - Levchuk, V. M.

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N2 - Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.

AB - Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field.

KW - Chevalley group

KW - Conjugately dense subgroup

KW - Locally finite field

KW - Monomial subgroup

KW - Parabolic subgroup

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JF - Siberian Mathematical Journal

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