Diagram Groups
Diagram Groups

Author: Victor Guba

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 130

ISBN-13: 0821806394

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Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group F. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group F. In particular, the authors describe the centralizers of elements in F, prove that it has solvable conjugacy problems, etc.

Groups '93 Galway [and] St. Andrews
Groups '93 Galway [and] St. Andrews

Author: T. C. Hurley

Publisher: Cambridge University Press

Published: 1995

Total Pages: 321

ISBN-13: 0521477506

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This two-volume book contains selected papers from the international conference 'Groups 1993 Galway / St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. As with the Proceedings of the earlier 'Groups-St Andrews' conferences it is hoped that the articles in these Proceedings will, with their many references, prove valuable both to experienced researchers and also to new postgraduates interested in group theory.

The Group Fixed by a Family of Injective Endomorphisms of a Free Group
The Group Fixed by a Family of Injective Endomorphisms of a Free Group

Author: Warren Dicks

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 96

ISBN-13: 0821805649

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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. 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.