Abstract
Let π be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. A subgroup H of an abstract residually π group R is said to be conjugacy π-distinguished if whenever y β R, then y has a conjugate in H if and only if the same holds for the images of y and H in every quotient group R/N β π of R. We prove that in a group having a normal free subgroup Ξ¦ such that R/Ξ¦ is in π, every finitely generated subgroup is conjugacy π-distinguished. We also prove that finitely generated subgroups of limit groups, of Lyndon groups and certain one-relator groups are conjugacy distinguished (π here is the class of all finite groups).
The authors would like to thank Ashot Minasyan for very useful discussions on Section 3 that led to considerable improvement of the section.
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Β© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Sliceable groups and towers of fields
- Pro-Hall R-groups and groups discriminated by the free pro-p group
- Filtrations of free groups arising from the lower central series
- Prosolvability criteria and properties of the prosolvable radical via Sylow sequences
- Non-commutative lattice problems
- Conjugacy distinguished subgroups
- Diophantine questions in the class of finitely generated nilpotent groups
- Uncountably many non-commensurable finitely presented pro-p groups
- Singer torus in irreducible representations of GL(n,q)
- Virtually free pro-p products
Articles in the same Issue
- Frontmatter
- Sliceable groups and towers of fields
- Pro-Hall R-groups and groups discriminated by the free pro-p group
- Filtrations of free groups arising from the lower central series
- Prosolvability criteria and properties of the prosolvable radical via Sylow sequences
- Non-commutative lattice problems
- Conjugacy distinguished subgroups
- Diophantine questions in the class of finitely generated nilpotent groups
- Uncountably many non-commensurable finitely presented pro-p groups
- Singer torus in irreducible representations of GL(n,q)
- Virtually free pro-p products