eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
102:1
102:19
10.4230/LIPIcs.ICALP.2020.102
article
Hardness of Equations over Finite Solvable Groups Under the Exponential Time Hypothesis
Weiß, Armin
1
https://orcid.org/0000-0002-7645-5867
Universität Stuttgart, Institut für Formale Methoden der Informatik (FMI), Germany
Goldmann and Russell (2002) initiated the study of the complexity of the equation satisfiability problem in finite groups by showing that it 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 of Fitting length two. In this work, we present the first lower bounds for the equation satisfiability problem in finite solvable groups: under the assumption of the exponential time hypothesis, we show that it cannot be in 𝖯 for any group of Fitting length at least four and for certain groups of Fitting length three. Moreover, the same hardness result applies to the equation identity problem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.102/LIPIcs.ICALP.2020.102.pdf
equations in groups
solvable groups
exponential time hypothesis