Equation satisfiability in solvable groups
Computational Complexity
2020-10-23 v1 Group Theory
Abstract
The study of the complexity of the equation satisfiability problem in finite groups had been initiated by Goldmann and Russell (2002) where they showed that this problem is in polynomial time 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 having a nilpotent normal subgroup with nilpotent factor . This paper shows that such normal subgroup must exist in each finite group with equation satisfiability solvable in polynomial time, unless the Exponential Time Hypothesis fails.
Keywords
Cite
@article{arxiv.2010.11788,
title = {Equation satisfiability in solvable groups},
author = {Paweł Idziak and Piotr Kawałek and Jacek Krzaczkowski and Armin Weiß},
journal= {arXiv preprint arXiv:2010.11788},
year = {2020}
}