Higman Embeddings and the Conjugacy Problem
by
Alexander Olshanskii
Vanderbilt University, Moscow State University
Coauthors: Mark Sapir (Vanderbilt University)

We prove that a finitely generated group G with solvable conjugacy problem is embeddable into a finitely presented group with solvable conjugacy problem. Furthermore our construction preserves the degree of unsolvability of the conjugacy problem (if it is unsolvable for G). This solves a problem posed by D.Collins in 1976.

A subgroup G of a group H is called Frattini embedded if any two elements of G that are conjugate in H are also cojugate in G. Our construction provides Frattini embeddings.

Paper reference: arXiv:math.GR/0212227

Date received: October 20, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajt-11.