Finite groups of outer automorphisms of free groups
In 1989 V. D. Mazurov and D. G. Khramtsov have completed the classification of finite groups of outer automorphisms of a finitely generated free group \(F_ n\) in relation to its rank \(n\) up to isomorphism. The list of such groups consists of 1) all subgroups of direct products \(H_ \nu = \prod^ s_{i = 1} (S_{m_ i}\wr_ \pi S_{k_ i})\) of permutation wreath products \(S_{m_ i}\wr_ \pi S_{k_ i}\) of symmetric groups \(S_{m_ i}\) and \(S_{k_ i}\) for any set \(\nu\) of integers \(m_ i \geq 2\), \(k_ i \geq 1\), \(i = 1,\dots,s\), satisfying \(\sum^ s_{i = 1}(m_ i - 1)k_ i \leq n\), 2) all subgroups of \(S_{n+1} \times Z_ 2\), 3) two exceptional subgroups for \(n = 10\). The proof of this result depended on parts of the classification of finite simple groups (CFSG). The paper under review eliminates this problem by giving a proof independent of CSFG.
scientific article; zbMATH DE number 56506