The automorphism tower of a free group

1997/11/24 by Vladimir Tolstykh, Tolstykh, Vladimir · 2 citations
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.math/9711203

arxiv created 1997/11/24 · arxiv updated 2009/11/30

Abstract

We prove that the automorphism group of an arbitrary non-abelian free group is complete. It generalizes the result by J.Dyer and E.Formanek (1975) stating the completeness of automorphism group of finitely generated free groups. Using the description of involutions in automorphism groups of free groups (J. Dyer, P. Scott, 1975) we obtain a group-theoretic characterization of inner automorphisms determined by primitive elements in the automorphism group of any non-abelian free group F. It follows that the subgroup Inn(F) is characteristic in Aut(F), and hence the latter one is complete.

Cited by

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

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