2016/03/18 by Attila Földvári, Földvári, Attila
Computer Science · Mathematics · #16N40 #20F10 #20G40 #68Q17 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1603.05788
openalex publication_date 2016/03/18 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The complexity of the equation solvability problem is known for nilpotent\ngroups, for not solvable groups and for some semidirect products of Abelian\ngroups. We provide a new polynomial time algorithm for deciding the equation\nsolvability problem over certain semidirect products, where the first factor is\nnot necessarily Abelian. Our main idea is to represent such groups as matrix\ngroups, and reduce the original problem to equation solvability over the\nunderlying field. Further, we apply this new method to give a much more\nefficient algorithm for equation solvability over nilpotent rings than\npreviously existed.\n