A Characterization of Periodic Automorphisms of a Free Group
نویسنده
چکیده
Let 9 be an automorphism of finite order of a free group X. We characterise the action of 9 on X by showing that X has a free basis which is the disjoint union of finite subsets Sj, where if S,, ~ {uq, «,,..., uk) then u¡9 ~ ul+x (0 < 1 < k) and uk9 = AjUqBj for some A}, B¡ in X and e = ±1. 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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