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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
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 Click above image for expanded view 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.

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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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.

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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