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

Bergman, George

doi:10.1090/S0002-9947-99-02087-5

Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups
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by George M. Bergman

Trans. Amer. Math. Soc. 351 (1999), 1531-1550

DOI: https://doi.org/10.1090/S0002-9947-99-02087-5

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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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