Fixed Subgroups of Endomorphisms of Free Products

2006/06/07 by Mihalis Sykiotis, Sykiotis, Mihalis
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.math/0606159

Abstract

Let G=∗_i=1ⁿG_i and let ϕ be a symmetric endomorphism of G. If ϕ is a monomorphism or if G is a finitely generated residually finite group, then the fixed subgroup Fix(ϕ)=\g∈ G:ϕ(g)=g\ of ϕ has Kurosh rank at most n.

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