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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups
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by George M. Bergman PDF
Trans. Amer. Math. Soc. 351 (1999), 1531-1550 Request permission

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
  • 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.
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1531-1550
  • MSC (1991): Primary 20E05, 20E06, 20J05; Secondary 05E20, 20C07, 20E08
  • DOI: https://doi.org/10.1090/S0002-9947-99-02087-5
  • MathSciNet review: 1458296