COMPLEXITY OF ISOMORPHISM TESTING.
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.
Annual Symposium on Foundations of Computer Science (Proceedings)
Garzon, M., & Zalcstein, Y. (1986). COMPLEXITY OF ISOMORPHISM TESTING.. Annual Symposium on Foundations of Computer Science (Proceedings), 313-321. https://doi.org/10.1109/sfcs.1986.53