Black-box group algorithm for group isomorphism problem

Idea and outline
The approach is as follows. Note that each step takes $$O(N^{s+1}s)$$ (multiplied by the time taken for group operations) time, hence the total is also $$O(N^{s+1}s)$$:


 * 1) Use the black-box group algorithm for generating set-finding problem to find a generating set of minimum size for $$G_1$$.
 * 2) Try every possible subset of $$G_2$$ of the same size and every possible bijection from the generating set of $$G_1$$ to that. The number of possibilities is $$O(N^s)$$. Use the black-box group algorithm for checking whether a bijection between generating sets extends to a group isomorphism to determine whether that bijection extends to a group isomorphism. This takes time $$O(Ns)$$ times the time taken for group operations.