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Maximum Order of Periodic Outer Automorphisms of a Free Group

✍ Scribed by Zhiqiang Bao

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 143 KB
Volume: 224
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8074

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✦ Synopsis

Let F n be a free group with rank n, and denote by Out F n its outer automorphism group. For arbitrary n, consider the orders of periodic elements in Out F n or, equivalently, the orders of finite cyclic subgroups of Out F n . By considering group actions on finite connected graphs, we obtained the number-theoretical characterization of these orders. Comparing the results with those for cyclic subgroups of finite symmetric groups asymptotic estimation for the maximum order c n is derived.

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