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The extended equivalence and equation solvability problems for groups

Abstract : 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.
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Gabor Horvath, Csaba Szabo. The extended equivalence and equation solvability problems for groups. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2011, Vol. 13 no. 4 (4), pp.23--32. ⟨hal-00990480⟩

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