## 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.## References

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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