The automorphism group of a free product of finite groups
The author studies the virtual cohomological dimension vcd(Out G) of the outer automorphism group Out G of a free product \(G=*G_ i\) of n finite groups. This is motivated by the papers by \textit{S. M. Gersten} [Preprint, Univ. Utah] and \textit{M. Culler} and \textit{K. Vogtmann} [Invent. Math. 84, 91-119 (1986; Zbl 0589.20022)] who proved that the outer automorphism group of a free group \(F_ n\) of rank n has vcd(Out \(F_ n)=2n-3\). In this paper the author proves that the group Out G has finite virtual cohomological dimension, and conjectures that vcd(Out G)\(=n-2\), where G is a free product of n finite groups, and proves this for \(n=3\). The proof is achieved by embedding Out G in the outer automorphism group of a free group of finite rank.
scientific article; zbMATH DE number 4067204