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

 

Supports of derivations, free factorizations,
and ranks of fixed subgroups in free groups


Author: George M. Bergman
Journal: Trans. Amer. Math. Soc. 351 (1999), 1531-1550
MSC (1991): Primary 20E05, 20E06, 20J05; Secondary 05E20, 20C07, 20E08
MathSciNet review: 1458296
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Abstract | References | Similar Articles | Additional Information

Abstract: For $F$ a free group of finite rank, it is shown that the fixed subgroup of any set $B$ of endomorphisms of $F$ has rank $\leq \operatorname {rank}(F)$, generalizing a recent result of Dicks and Ventura. The proof involves the combinatorics of derivations of groups. Some related questions are examined.


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Additional Information

George M. Bergman
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: gbergman@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02087-5
PII: S 0002-9947(99)02087-5
Received by editor(s): April 5, 1996
Received by editor(s) in revised form: April 8, 1997
Additional Notes: This work was done while the author was partly supported by NSF contract DMS\ 93-03379.
Article copyright: © Copyright 1999 American Mathematical Society