Contemporary Mathematics 1996; 81 pp; softcover Volume: 195 ISBN10: 0821805649 ISBN13: 9780821805640 List Price: US$23 Member Price: US$18.40 Order Code: CONM/195
 This monograph contains a proof of the BestvinaHandel 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 selfcontained, 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 BestvinaHandel 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 BestvinaHandel is translated into the language of groupoids, and many details previously left to the reader are meticulously verified in this text. Readership Graduate students and research mathematicians interested in finite group theory; also suitable as a supplementary text for combinatorial group theory courses. Table of Contents  Groupoids
 Measuring devices
 Properties of the basic operations
 Minimal representatives and fixed subgroupoids
 Open problems
 Bibliography
 Index
