Conjugately dense subgroups of free products of groups with amalgamation

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Abstract

A subgroup having non-empty intersection with each class of conjugate elements of the group is said to be conjugately dense. It is shown that, under certain conditions, the number of conjugately dense subgroups in a free product with amalgamation is not less than some cardinal. As a consequence, P. Neumann's conjecture in the Kourovka notebook (Question 6.38) is refuted. It is also stated that a modular group and a non-Abelian group of countable or finite rank possess continuum many pairwise non-conjugate conjugately dense subgroups.

Original languageEnglish
Pages (from-to)296-305
Number of pages10
JournalAlgebra and Logic
Volume45
Issue number5
DOIs
Publication statusPublished - Sep 2006

Keywords

  • Conjugately dense subgroup
  • Field with discrete valuation
  • Free product with amalgamation
  • Linear group

ASJC Scopus subject areas

  • Algebra and Number Theory

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