Electronic ISBN:  9781470404055 
Product Code:  MEMO/170/804.E 
133 pp 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $40.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 170; 2004MSC: 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.
ReadershipGraduate 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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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