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 |
|---|---|
| Pages (from-to) | 296-305 |
| Number of pages | 10 |
| Journal | Algebra and Logic |
| Volume | 45 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Sep 2006 |
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Keywords
- Conjugately dense subgroup
- Field with discrete valuation
- Free product with amalgamation
- Linear group
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Conjugately dense subgroups of free products of groups with amalgamation. / Zyubin, S. A.
In: Algebra and Logic, Vol. 45, No. 5, 09.2006, p. 296-305.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Conjugately dense subgroups of free products of groups with amalgamation
AU - Zyubin, S. A.
PY - 2006/9
Y1 - 2006/9
N2 - 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.
AB - 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.
KW - Conjugately dense subgroup
KW - Field with discrete valuation
KW - Free product with amalgamation
KW - Linear group
UR - http://www.scopus.com/inward/record.url?scp=33750705624&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33750705624&partnerID=8YFLogxK
U2 - 10.1007/s10469-006-0028-1
DO - 10.1007/s10469-006-0028-1
M3 - Article
AN - SCOPUS:33750705624
VL - 45
SP - 296
EP - 305
JO - Algebra and Logic
JF - Algebra and Logic
SN - 0002-5232
IS - 5
ER -