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Higman embedding preserving the solvability of conjugacy problem
by
Mark Sapir
Vanderbilt University
Coauthors: A.Yu. Olshanskii
We prove that every finitely generated group with solvable conjugacy problem can be embedded into a finitely presented group with solvable conjugacy problem. Moreover our embedding preserves the degree of solvability of the conjugacy problem and the finitely generated subgroup is embedded without distortion.
This solves an old problem by D. Collins. As a corollary we prove that every finitely generated group with solvable order and power problems can be embedded without distortion into a finitely presented group with solvable order, power and conjugacy problems.
I will show how this and similar embeddings can help solving some other long standing group theoretic problems.
Date received: March 14, 1999
Copyright © 1999 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 # caca-70.