# Finding a cycle base of a permutation group

## TL;DR

This paper introduces a polynomial-time algorithm for constructing a cycle base of a permutation group, which is a maximal set of pairwise non-conjugate regular cyclic subgroups, advancing computational group theory.

## Contribution

It provides the first known polynomial-time method to find a cycle base of permutation groups, improving the efficiency of analyzing their structure.

## Key findings

- Cycle base can be constructed in polynomial time
- Algorithm efficiently finds maximal non-conjugate regular cyclic subgroups
- Advances computational methods in permutation group analysis

## Abstract

A cycle base of a permutation group is defined to be a maximal set of its pairwise non-conjugate regular cyclic subgroups. It is proved that a cycle base of a permutation group of degree $n$ can be constructed in polynomial time in~$n$.