**Memoirs of the American Mathematical Society**

2004;
133 pp;
Softcover

MSC: Primary 20;

Print ISBN: 978-0-8218-3513-5

Product Code: MEMO/170/804

List Price: $68.00

AMS Member Price: $40.80

MAA Member Price: $61.20

**Electronic ISBN: 978-1-4704-0405-5
Product Code: MEMO/170/804.E**

List Price: $68.00

AMS Member Price: $40.80

MAA Member Price: $61.20

# The Conjugacy Problem and Higman Embeddings

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*A. Yu. Ol’shanskii; M. V. Sapir*

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

# Table of Contents

## The Conjugacy Problem and Higman Embeddings

- Contents v6 free
- 1 Introduction 110 free
- 2 List of relations 1019 free
- 3 The first properties of H 2231
- 4 The group H[sub(2)] 3746
- 5 The word problem in H[sub(1)] 4251
- 6 Some special diagrams 4857
- 7 Computations of S ∪ S 6069
- 8 Spirals 8695
- 9 Rolls 97106
- 10 Arrangement of hubs 122131
- 11 The end of the proof 127136
- References 128137
- Subject index 131140