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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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A characterization of periodic automorphisms of a free group
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by James McCool PDF
Trans. Amer. Math. Soc. 260 (1980), 309-318 Request permission

Abstract:

Let $\theta$ be an automorphism of finite order of a free group X. We characterise the action of $\theta$ on X by showing that X has a free basis which is the disjoint union of finite subsets ${S_j}$, where if ${S_j} = \{ {u_0}, {u_1}, \ldots , {u_k}\}$ then ${u_i}\theta = {u_{i + 1}} (0 \leqslant 1 < k)$ and ${u_k}\theta = {A_j}u_0^e{B_j}$ for some ${A_j}$, ${B_j}$ in X and $\varepsilon = \pm 1$. 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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • 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