Non-CLT groups of order $pq^3$

TL;DR

This paper characterizes finite groups of order pq^3 that do not satisfy the Converse of Lagrange's Theorem, providing insights into their structure and properties.

Contribution

It offers a new characterization of non-CLT groups of order pq^3, expanding understanding of group order and subgroup relationships.

Findings

Identifies conditions under which groups of order pq^3 fail CLT

Classifies non-CLT groups within this order category

Enhances understanding of subgroup structures in finite groups

Abstract

In this note we give a characterization of finite groups of order $pq^3$ ($p$, $q$ primes) that fail to satisfy the Converse of Lagrange's Theorem.