Finding cycle types in permutation groups with few generators
Group Theory
2025-03-05 v1
Abstract
The problem whether a given permutation group contains a permutation with a given cycle type is studied. This problem is known to be NP-complete. In this paper it is shown that the problem can be solved in logspace for a cyclic permutation group and that it is NP-complete for a 2-generated abelian permutation group. In addition it is shown that it is NP-complete whether a 2-generated abelian permutation group contains a fixpoint-free permutation.
Keywords
Cite
@article{arxiv.2503.02864,
title = {Finding cycle types in permutation groups with few generators},
author = {Markus Lohrey and Andreas Rosowski},
journal= {arXiv preprint arXiv:2503.02864},
year = {2025}
}