Small conjugacy classes in the automorphism groups of relatively free groups
Group Theory
2010-03-26 v1
Abstract
Let F be an infinitely generated free group and R a fully invariant subgroup of F such that (a) R is contained in the commutator subgroup F' of F and (b) the quotient group F/R is residually torsion-free nilpotent. Then the automorphism group Aut(F/R') of the group F/R' is complete. In particular, the automorphism group of any infinitely generated free solvalbe group of derived length at least two is complete. This extends a result by Dyer and Formanek (1977) on finitely generated groups F_n/R' where F_n is a free group of finite rank n at least two and R a characteristic subgroup of F_n.
Keywords
Cite
@article{arxiv.1003.4762,
title = {Small conjugacy classes in the automorphism groups of relatively free groups},
author = {Vladimir Tolstykh},
journal= {arXiv preprint arXiv:1003.4762},
year = {2010}
}
Comments
15pp.