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Virtually free groups with finitely many outer automorphisms
Author(s):
Martin
R.
Pettet
Journal:
Trans. Amer. Math. Soc.
349
(1997),
4565-4587.
MSC (1991):
Primary 20F28;
Secondary 20E36, 20E08
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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 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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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