Basis-conjugating automorphisms of a free group
The paper extends the investigations undertook by the author in an earlier paper [Vestn. Mosk. Univ., Ser. I 1996, No. 1, 32-36 (1996; Zbl 0881.70002)]. In this paper it is proved that the group \({\mathfrak M}_n\) is a semidirect product of the (normal) subgroup \({\mathfrak C}_n\) and the subgroup \({\mathfrak M}_{n-1}\). Also it is shown that the group \({\mathfrak C}_n\) is the centralizer of the group \({\mathfrak M}_{n-1}\) in the group \({\mathfrak M}_n\) and in the group \({\mathfrak M}_n\) the centralizer of the group \({\mathfrak N}_n\) coincides with the centre of the group \({\mathfrak N}_n\) when \(n>2\).
scientific article; zbMATH DE number 1134954