Diagram Groups

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  • Diagram Groups Book Detail

  • Author : Victor Guba
  • Release Date : 1997
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 130
  • ISBN 13 : 0821806394
  • File Size : 18,18 MB

Diagram Groups by Victor Guba PDF Summary

Book Description: 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.

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