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 language | English |
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Pages (from-to) | 296-305 |
Number of pages | 10 |
Journal | Algebra and Logic |
Volume | 45 |
Issue number | 5 |
DOIs | |
Publication status | Published - Sep 2006 |
Keywords
- Conjugately dense subgroup
- Field with discrete valuation
- Free product with amalgamation
- Linear group
ASJC Scopus subject areas
- Algebra and Number Theory