A characterization of periodic automorphisms of a free group

Author:
James McCool

Journal:
Trans. Amer. Math. Soc. **260** (1980), 309-318

MSC:
Primary 20E05; Secondary 20E36

DOI:
https://doi.org/10.1090/S0002-9947-1980-0570792-1

MathSciNet review:
570792

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Abstract: Let be an automorphism of finite order of a free group *X*. We characterise the action of on *X* by showing that *X* has a free basis which is the disjoint union of finite subsets , where if then and for some , in *X* and . As an application of this result, we obtain a list of the conjugacy classes of periodic automorphisms of the free group of rank three.

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DOI:
https://doi.org/10.1090/S0002-9947-1980-0570792-1

Article copyright:
© Copyright 1980
American Mathematical Society