Twisted conjugacy separable groups
Group Theory
2012-05-04 v3 Logic
Abstract
We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this property and study its behavior under some extensions. An affirmative answer to the twisted Dehn conjugacy problem for polycyclic-by-finite group is obtained. Some problems for the further study are indicated.
Cite
@article{arxiv.math/0606764,
title = {Twisted conjugacy separable groups},
author = {Alexander Fel'shtyn and Evgenij Troitsky},
journal= {arXiv preprint arXiv:math/0606764},
year = {2012}
}
Comments
v3: Theorem 9.1 corrected, Section 9 rewritten. v2: Sect.9 about residually finite groups is added, giving an affirmative answer to Quest.4 of Sect.8. Some refinements on the twisted Dehn conjugacy problem are added in Sect.7. Related changes are made, mostly in Introduction