We consider a group G with an automorphism of finite, usu- ally prime, order. If G has finite Hirsch number, and also if G satisfies various stronger rank restrictions, we study the consequences and equivalent hypotheses of having only finitely many fixed-points. In particular we prove that if a group G with finite Hirsch number h admits an automorphism ϕ of prime order p such that |CG (ϕ)| = n < ∞, then G has a subgroup of finite index bounded in terms of p, n and h that is nilpotent of p-bounded class.

Groups Admitting an Automorphism of Prime Order with Finite Centralizer

JABARA, Enrico;
2014-01-01

Abstract

We consider a group G with an automorphism of finite, usu- ally prime, order. If G has finite Hirsch number, and also if G satisfies various stronger rank restrictions, we study the consequences and equivalent hypotheses of having only finitely many fixed-points. In particular we prove that if a group G with finite Hirsch number h admits an automorphism ϕ of prime order p such that |CG (ϕ)| = n < ∞, then G has a subgroup of finite index bounded in terms of p, n and h that is nilpotent of p-bounded class.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/39506
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