isomorphism tests for (p-)groups
kind: discussion
Taking the problem(s) described in gap-packages/anupq/issues/32 into account, is it a good idea to delegate, in the case of p-groups `G` and `H`, from `IsomorphismGroups( G, H )` to `IsomorphismPGroups( G, H )`, which then calls ANUPQ's functions?
Perhaps the answer is yes because other GAP methods also cannot do better if ANUPQ runs into problems.
Currently this delegation happens if ANUPQ is available and the groups have equal order larger than 2000.
Independent of that, should we perhaps introduce `IsIsomorphicGroups( G, H )` for two groups `G` and `H`, returning `true` if `G` and `H` are isomorphic, and `false` otherwise?
This would be analogous to the `IsIsomorphicPGroups` function from the ANUPQ package, a nonconstructive test that avoids creating an isomorphism if one does not need it.
For example, if `IdGroup` is available for `G` and `H` then `IdGroup` yields a decision without creating an isomorphism, and this is often very fast.
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