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The Conjugacy Problem and Higman Embeddings
A. Yu. Ol'shanskii, Moscow State University, Russia, and M. V. Sapir, Vanderbilt University, Nashville, TN

Memoirs of the American Mathematical Society
2004; 133 pp; softcover
Volume: 170
ISBN-10: 0-8218-3513-0
ISBN-13: 978-0-8218-3513-5
List Price: US$68
Individual Members: US$40.80
Institutional Members: US$54.40
Order Code: MEMO/170/804
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For every finitely generated recursively presented group \(\mathcal G\) we construct a finitely presented group \(\mathcal H\) containing \(\mathcal G\) such that \(\mathcal G\) is (Frattini) embedded into \(\mathcal H\) and the group \(\mathcal H\) has solvable conjugacy problem if and only if \(\mathcal G\) has solvable conjugacy problem. Moreover \(\mathcal G\) and \(\mathcal H\) have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D. Collins.


Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

  • Introduction
  • List of relations
  • The first properties of \({\mathcal H}\)
  • The group \({\mathcal H}_2\)
  • The word problem in \({\mathcal H}_1\)
  • Some special diagrams
  • Computations of \({\mathcal S} \cup {\bar{\mathcal S}}\)
  • Spirals
  • Rolls
  • Arrangement of hubs
  • The end of the proof
  • References
  • Subject index
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