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Conjugacy distinguished subgroups

  • Luis Ribes EMAIL logo and Pavel A. Zalesskii
Published/Copyright: April 9, 2016

Abstract

Let π’ž be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. A subgroup H of an abstract residually π’ž group R is said to be conjugacy π’ž-distinguished if whenever y ∈ 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 ∈ π’ž of R. We prove that in a group having a normal free subgroup Ξ¦ such that R/Ξ¦ is in π’ž, every finitely generated subgroup is conjugacy π’ž-distinguished. We also prove that finitely generated subgroups of limit groups, of Lyndon groups and certain one-relator groups are conjugacy distinguished (π’ž 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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Received: 2015-4-12
Published Online: 2016-4-9
Published in Print: 2016-5-1

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