Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups
by
Ilya Kapovich
University of Illinois at Urbana-Champaign
Coauthors: Paul Schupp

We prove that there is an exponentially generic (in the sense of Ol'shanskii) class of one-relator groups for which the isomorphism problem is solvable in exponential time, as is the problem of deciding if a given one-relator presentation belongs to this class. We obtain this fact as a corollary of a more general result that a "random" (i.e. generic) n-generated m-related group has exactly one Nielsen-equivalence class of generating n-tuples (where n > 1, m > 0 are arbitrary fixed integers).

Paper reference: arXiv:math.GR/0210307

Date received: October 5, 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-04.