To the problem of irreducible conjugately dense subgroups of linear groups

Research output: Contribution to journalArticle

Abstract

The existence of conjugately dense subgroups in amalgamated free products is studied. A subgroup intersecting each conjugacy class in a group is said to be conjugately dense. Any modular group and any free non-Abelian group of countable or finite rank has continuum many pairwise nonconjugate conjugately dense subgroups. The subgroups decomposes into amalgamated free products, if a field has a nontrivial discrete valuation. All proper maximal reducible subgroups of the locally finite groups are conjugate to each other. The conjugately dense subgroups constructed theoretically are free and irreducible, and the Neumann's conjecture is false for the locally finite groups over a specified field.

Original languageEnglish
Pages (from-to)266-269
Number of pages4
JournalDoklady Mathematics
Volume75
Issue number2
DOIs
Publication statusPublished - 1 Apr 2007

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Linear Group
Subgroup
Amalgamated Free Product
Locally Finite Groups
Modular Group
Finite Rank
Conjugacy class
Valuation
Countable
Pairwise
Continuum
Decompose

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

To the problem of irreducible conjugately dense subgroups of linear groups. / Zyubin, S. A.

In: Doklady Mathematics, Vol. 75, No. 2, 01.04.2007, p. 266-269.

Research output: Contribution to journalArticle

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