1986•Unpublished venueRequires access

The complexity of isomorphism testing

Max Garzón, Yechezkel Zalcstein

Abstract

A polynomial time isomorphism test for a class of groups, properly containing the class of abelian groups, is presented. Isomorphism testing of group presentations for (a subclass of) the same class of groups is shown to be (graph) isomorphism complete. These seem to be the first known isomorphism complete problems in group theory. Subexponential tests are presented as well for rings and algebras.

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Key concepts: Graph isomorphism, Isomorphism (crystallography), Group isomorphism, Subclass, Induced subgraph isomorphism problem, Mathematics, Abelian group, Class (philosophy)