Virtually free groups with finitely many outer automorphisms
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- by Martin R. Pettet PDF
- Trans. Amer. Math. Soc. 349 (1997), 4565-4587 Request permission
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.References
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Additional Information
- Martin R. Pettet
- Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606
- Email: mpettet@math.utoledo.edu
- Received by editor(s): November 4, 1994
- Received by editor(s) in revised form: January 4, 1966
- © Copyright 1997 American Mathematical Society
- 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