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JOURNALS // Algebra i Analiz // Archive

Algebra i Analiz, 2007 Volume 19, Issue 2, Pages 74–85 (Mi aa113)

This article is cited in 3 papers

Research Papers

Automorphisms of a free group of infinite rank

C. K. Guptaa, W. Hołubowskib

a Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada
b Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

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 $\mathrm{Aut}F_{\infty}$ 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.

Keywords: Free group of infinite rank, automorphism group, string.

MSC: 20E05

Received: 19.06.2006

Language: English


 English version:
St. Petersburg Mathematical Journal, 2008, 19:2, 215–223

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© Steklov Math. Inst. of RAS, 2025