English

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}
}
R2 v1 2026-06-28T22:06:50.253Z