Recursively enumerable degrees and the conjugacy problem

The principal result obtained is the theorem tha t for every recursively enumerable degree of unsolvability, there exists a finitely presented group whese con jugacy problem has tha t degree. (Parts I, I I , I I I and IV.) In Par t V this result is generalised to the theorem tha t certain complexes of recursively enumerable degrees of unsolvabil i ty m a y be obtained as the degrees of a complex of problems concerning conjugacy in a finitely presented group. I t is a pleasure to acknowledge the encouragement and inspiration provided by Professor William Boone during this work.