# The Group Fixed by a Family of Injective Endomorphisms of a Free Group (Contemporary Mathematics)

By: Warren Dicks (author), Enric Ventura (author)Paperback

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£23.95

### Description

This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank $n$, the fixed group has rank at most $n$) that to date has not been available in book form. The account is self-contained, simplified, purely algebraic, and extends the results to an arbitrary family of injective endomorphisms. Let $F$ be a finitely generated free group, let $\phi$ be an injective endomorphism of $F$, and let $S$ be a family of injective endomorphisms of $F$.By using the Bestvina-Handel argument with graph pullback techniques of J. R. Stallings, the authors show that, for any subgroup $H$ of $F$, the rank of the intersection $H\cap \mathrm {Fix}(\phi)$ is at most the rank of $H$. They deduce that the rank of the free subgroup which consists of the elements of $F$ fixed by every element of $S$ is at most the rank of $F$. The topological proof by Bestvina-Handel is translated into the language of groupoids, and many details previously left to the reader are meticulously verified in this text.

### Contents

Groupoids Measuring devices Properties of the basic operations Minimal representatives and fixed subgroupoids Open problems Bibliography Index.

### Product Details

• ISBN13: 9780821805640
• Format: Paperback
• Number Of Pages: 81
• ID: 9780821805640
• ISBN10: 0821805649

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