Equation Satisfiability in Solvable Groups
Paweł Idziak, Piotr Kawałek, Jacek Krzaczkowski, Armin Weiß · Theory of Computing Systems · 2022
Abstract The 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, 2002) where they showed that this problem is in for nilpotent groups while it is -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.