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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Virtually free groups
with finitely many outer automorphisms


Author: Martin R. Pettet
Journal: Trans. Amer. Math. Soc. 349 (1997), 4565-4587
MSC (1991): Primary 20F28; Secondary 20E36, 20E08
MathSciNet review: 1370649
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Abstract: Let $G$ be a finitely generated virtually free group. From a presentation of $G$ as the fundamental group of a finite graph of finite-by-cyclic groups, necessary and sufficient conditions are derived for the outer automorphism group of $G$ 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 $G$-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/S0002-9947-97-01699-1
PII: S 0002-9947(97)01699-1
Received by editor(s): November 4, 1994
Received by editor(s) in revised form: January 4, 1966
Article copyright: © Copyright 1997 American Mathematical Society