Finite primitive permutation groups containing a permutation having at most four cycles

TL;DR

This paper classifies finite primitive permutation groups that include a permutation with at most four cycles, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete classification of finite primitive groups containing permutations with limited cycle structures, advancing the understanding of permutation group theory.

Findings

Complete classification of such groups

Identification of structural properties of permutations with few cycles

Implications for symmetry and group actions

Abstract

We classify the finite primitive groups containing a permutation with at most four cycles (including fixed points) in its disjoint cycle representation.