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special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity We prove that the extended equivalence problem is solvable in polynomial time for finite nilpotent groups, and coNP-complete, otherwise. We prove that the extended equation solvability problem is solvable in polynomial time for finite nilpotent groups, and NP-complete, otherwise.

The extended equivalence and equation solvability problems for groups