Geodesic
On Basis-Conjugating Automorphisms of Free Groups
Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1525-1529

Voir la notice de l'article provenant de la source Cambridge University Press

Let X = {x 1, ... xn } be a free generating set of the free group Fn and let H be the subgroup of Aut Fn consisting of those automorphisms α such that α(xi ) is conjugate to xi for each i = 1, 2 , ..., n. We call H the Z-conjugating subgroup of Aut Fn . In [1] Humphries found a generating set for the isomorphic copy H 1 of H consisting of Nielsen transformations where each is conjugate to ui (see remark 1 below). The purpose of this paper is to find a presentation of H (and hence of H 1).Let i ≠ j be elements of {1, 2, ..., n}. We denote by (xi ; xj ) the automorphism of Fn which sends xi to and fixes xk if k ≠ i. Let S be the set of all such automorphisms. 
McCool, J. On Basis-Conjugating Automorphisms of Free Groups. Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1525-1529. doi: 10.4153/CJM-1986-073-3
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