Virtually free groups with finitely many outer automorphisms
Author:
Martin R. Pettet
Journal:
Trans. Amer. Math. Soc. 349 (1997), 45654587
MSC (1991):
Primary 20F28; Secondary 20E36, 20E08
MathSciNet review:
1370649
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Abstract: Let be a finitely generated virtually free group. From a presentation of as the fundamental group of a finite graph of finitebycyclic groups, necessary and sufficient conditions are derived for the outer automorphism group of to be finite. Two versions of the characterization are given, both effectively verifiable from the graph of groups. The more purely group theoretical criterion is expressed in terms of the structure of the normalizers of the edge groups (Theorem 5.10); the other version involves certain finiteness conditions on the associated tree (Theorem 5.16). Coupled with an earlier result, this completes a description of the finitely generated groups whose full automorphism groups are virtually free.
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Additional Information
Martin R. Pettet
Affiliation:
Department of Mathematics, University of Toledo, Toledo, Ohio 43606
Email:
mpettet@math.utoledo.edu
DOI:
http://dx.doi.org/10.1090/S0002994797016991
PII:
S 00029947(97)016991
Received by editor(s):
November 4, 1994
Received by editor(s) in revised form:
January 4, 1966
Article copyright:
© Copyright 1997
American Mathematical Society
