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 language | English |
|---|---|
| Pages (from-to) | 266-269 |
| Number of pages | 4 |
| Journal | Doklady Mathematics |
| Volume | 75 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2007 |
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ASJC Scopus subject areas
- Mathematics(all)
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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 journal › Article
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TY - JOUR
T1 - To the problem of irreducible conjugately dense subgroups of linear groups
AU - Zyubin, S. A.
PY - 2007/4/1
Y1 - 2007/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=34248332114&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34248332114&partnerID=8YFLogxK
U2 - 10.1134/S1064562407020226
DO - 10.1134/S1064562407020226
M3 - Article
AN - SCOPUS:34248332114
VL - 75
SP - 266
EP - 269
JO - Doklady Mathematics
JF - Doklady Mathematics
SN - 1064-5624
IS - 2
ER -