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The Conjugacy Problem and Higman Embeddings
 
A. Yu. Ol’shanskii Moscow State University, Moscow, Russia
M. V. Sapir Vanderbilt University, Nashville, TN
Front Cover for The Conjugacy Problem and Higman Embeddings
Available Formats:
Electronic ISBN: 978-1-4704-0405-5
Product Code: MEMO/170/804.E
133 pp 
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
Front Cover for The Conjugacy Problem and Higman Embeddings
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  • Front Cover for The Conjugacy Problem and Higman Embeddings
  • Back Cover for The Conjugacy Problem and Higman Embeddings
The Conjugacy Problem and Higman Embeddings
A. Yu. Ol’shanskii Moscow State University, Moscow, Russia
M. V. Sapir Vanderbilt University, Nashville, TN
Available Formats:
Electronic ISBN:  978-1-4704-0405-5
Product Code:  MEMO/170/804.E
133 pp 
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1702004
    MSC: Primary 20;

    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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. List of relations
    • 3. The first properties of $\mathcal {H}$
    • 4. The group $\mathcal {H}_2$
    • 5. The word problem in $\mathcal {H}_1$
    • 6. Some special diagrams
    • 7. Computations of $\mathcal {S} \cup \bar {\mathcal {S}}$
    • 8. Spirals
    • 9. Rolls
    • 10. Arrangement of hubs
    • 11. The end of the proof
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Volume: 1702004
MSC: Primary 20;

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.

Readership

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

  • Chapters
  • 1. Introduction
  • 2. List of relations
  • 3. The first properties of $\mathcal {H}$
  • 4. The group $\mathcal {H}_2$
  • 5. The word problem in $\mathcal {H}_1$
  • 6. Some special diagrams
  • 7. Computations of $\mathcal {S} \cup \bar {\mathcal {S}}$
  • 8. Spirals
  • 9. Rolls
  • 10. Arrangement of hubs
  • 11. The end of the proof
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