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Maximum Order of Finite Abelian Subgroups in the Outer Automorphism Group of a Rank n Free Group

✍ Scribed by Zhiqiang Bao

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 128 KB
Volume: 236
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8486

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✦ Synopsis

Let F be a free group of rank n. Denote by Out F its outer automorphism n n group, that is, its automorphism group modulo its inner automorphism group. For arbitrary n, by considering group actions on finite connected graphs, we derived the maximum order of finite abelian subgroups in Out F . Moreover, it is shown n that the subgroups reaching this maximum order can be determined up to isomorphisms.

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✍ Zhiqiang Bao 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 143 KB

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