Small conjugacy classes in the automorphism groups of relatively free groups

2010/03/24 by Tolstykh, Vladimir · 2 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1003.4762

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.

Cited by

• On the outer automorphism groups of free groups
• Complete outer automorphism groups of free nilpotent groups

Related

• Free two-step nilpotent groups whose automorphism group is complete
• Isomorphism problem for finitely generated fully residually free groups
• Linear automorphism groups of relatively free groups
• Complete outer automorphism groups of free nilpotent groups
• The automorphism tower of a free group