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

• 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