43.10 Random Isomorphism Testing

The generic isomorphism test for groups may be applied to pc groups as well. However, this test is often quite time consuming. Here we describe another method to test isomorphism by a probabilistic approach.

This method takes a list of groups and a non-negative integer as input. The output is a sublist of the input list where only isomorphic copies have been removed. The integer gives a certain amount of control over the probability to detect all isomorphisms. If it is 0, then nothing will be done at all. The larger the integer is, the larger is the probability of finding all isomorphisms. However, due to the underlying method we can not guarantee that the algorithm finds all isomorphisms, no matter how large n is.