Automorphisms of a free group of infinite rank

Gupta, C.; Hołubowski, W.

doi:10.1090/S1061-0022-08-00994-1

Automorphisms of a free group of infinite rank
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by C. K. Gupta and W. Hołubowski

St. Petersburg Math. J. 19 (2008), 215-223

DOI: https://doi.org/10.1090/S1061-0022-08-00994-1

Published electronically: February 1, 2008

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Abstract:

The problem of classifying the automorphisms of a free group of infinite countable rank is investigated. Quite a reasonable generating set for the group $\operatorname {Aut}F_{\infty }$ is described. Some new subgroups of this group and structural results for them are presented. The main result says that the group of all automorphisms is generated (modulo the $IA$-automorphisms) by strings and lower triangular automorphisms.

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