Twisted conjugacy separable groups
Abstract
We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of BurnsideFrobenius 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 polycyclicbyfinite group is obtained. Some problems for the further study are indicated.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606764
 Bibcode:
 2006math......6764F
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Logic;
 20E45;
 20F10;
 03D40
 EPrint:
 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