Displaying similar documents to “Infinite soluble groups with no outer automorphisms”

Almost fixed-point-free automorphisms of prime order

Bertram Wehrfritz (2011)

Open Mathematics

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Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived...

On the derived length of parasoluble groups

Alessio Russo (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.