Memoirs of the American Mathematical Society 2004; 133 pp; softcover Volume: 170 ISBN10: 0821835130 ISBN13: 9780821835135 List Price: US$68 Individual Members: US$40.80 Institutional Members: US$54.40 Order Code: MEMO/170/804
 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
