On the non-existence of sharply transitive sets of permutations in certain finite permutation groups

TL;DR

This paper introduces a simple combinatorial method to prove that certain finite permutation groups cannot have sharply transitive sets of permutations, clarifying limitations in their structure.

Contribution

The paper provides a straightforward combinatorial approach to establish the non-existence of sharply transitive permutation sets in specific finite groups.

Findings

Demonstrates non-existence of sharply transitive sets in certain groups

Introduces a simple combinatorial trick for such proofs

Clarifies structural limitations of finite permutation groups

Abstract

In this short note we present a simple combinatorial trick which can be effectively applied to show the non--existence of sharply transitive sets of permutations in certain finite permutation groups.