gap
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Documentation of `ActionHomomorphism` is misleading
The documentation states this homomorphism is a permutation equivalence. Here this can be understood as meaning the return value of ActionHomomorphism. But it is easy to make ActionHomomorphism return a map which is not a permutation equivalence.
To make explicit what @ssiccha only hints at: What "permutation equivalence" really refers to the (implicit) permutation equivalence between Sym(Omega) and Sym(|Omega|). That should indeed be clarified.