Efficient Isomorphism Testing for a Class of Group Extensions

Abstract

The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism testing for nonabelian groups. In this paper we study this problem for a class of groups corresponding to one of the simplest ways of constructing nonabelian groups from abelian groups: the groups that are extensions of an abelian group A by a cyclic group of order m. We present an efficient algorithm solving the group isomorphism problem for all the groups of this class such that the order of A is coprime with m. More precisely, our algorithm runs in time almost linear in the orders of the input groups and works in the general setting where the groups are given as black-boxes.

17 pages, accepted to the STACS 2009 conference

Cited by in corpus (4)

• Bidirectional Collision Detection and Faster Deterministic Isomorphism Testing
• Breaking the n^(log n) Barrier for Solvable-Group Isomorphism
• An Efficient Quantum Algorithm for some Instances of the Group Isomorphism Problem
• On the Descriptive Complexity of Groups without Abelian Normal Subgroups (Extended Abstract)