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The Group Fixed by a Family of Injective Endomorphisms of a Free Group
35,70 €
American Mathematical Society
Sivumäärä: 81 sivua
Asu: Pehmeäkantinen kirja
Julkaisuvuosi: 1996, 01.01.1996 (lisätietoa)
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 $Hcap mathrm {Fix}(phi)$ 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.

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The Group Fixed by a Family of Injective Endomorphisms of a Free Group
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ISBN:
9780821805640
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