Idziak, PawełKawałek, PiotrKrzaczkowski, JacekWeiß, Armin2024-11-132024-11-1320221433-04901432-43501912192969http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-152703http://elib.uni-stuttgart.de/handle/11682/15270http://dx.doi.org/10.18419/opus-15251The study of the complexity of the equation satisfiability problem in finite groups had been initiated by Goldmann and Russell in (Inf. Comput. 178 (1), 253-262, 10 ) where they showed that this problem is in P for nilpotent groups while it is NP -complete for non-solvable groups. Since then, several results have appeared showing that the problem can be solved in polynomial time in certain solvable groups G having a nilpotent normal subgroup H with nilpotent factor G / H . This paper shows that such a normal subgroup must exist in each finite group with equation satisfiability solvable in polynomial time, unless the Exponential Time Hypothesis fails.eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/004510article2024-11-02