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

DOI:
https://doi.org/10.1090/S0002-9947-97-01699-1

MathSciNet review:
1370649

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finitely generated virtually free group. From a presentation of 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 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:
https://doi.org/10.1090/S0002-9947-97-01699-1

Received by editor(s):
November 4, 1994

Received by editor(s) in revised form:
January 4, 1966

Article copyright:
© Copyright 1997
American Mathematical Society