To the problem of irreducible conjugately dense subgroups of linear groups

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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

ASJC Scopus subject areas

  • Mathematics(all)

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