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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Automorphisms of a free group of infinite rank


Authors: C. K. Gupta and W. Hołubowski
Original publication: Algebra i Analiz, tom 19 (2007), nomer 2.
Journal: St. Petersburg Math. J. 19 (2008), 215-223
MSC (2000): Primary 20E05
Published electronically: February 1, 2008
MathSciNet review: 2333897
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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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Additional Information

C. K. Gupta
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 Canada

W. Hołubowski
Affiliation: Institute of Mathematics, Silesian University of Technology, Kaszubska, 23, 44-100 Gliwice, Poland
Email: w.holubowski@polsl.pl

DOI: https://doi.org/10.1090/S1061-0022-08-00994-1
Keywords: Free group of infinite rank, automorphism group, string
Received by editor(s): June 19, 2006
Published electronically: February 1, 2008
Article copyright: © Copyright 2008 American Mathematical Society