# A short note on the noncoprime regular module problem

## TL;DR

This paper investigates the existence of regular modules in a specific group action setting involving finite groups and automorphisms, contributing to the understanding of module structures under group actions.

## Contribution

It introduces a new perspective on the regular module problem for finite groups with automorphism actions, focusing on a particular configuration.

## Key findings

- Identifies conditions for the existence of regular A-modules in the given setting.
- Provides theoretical insights into automorphism actions on finite groups and modules.
- Clarifies the structure of semidirect products in the context of module theory.

## Abstract

We consider a special configuration in which a finite group $A$ acts by automorphisms on the finite group $G$, and the semidirect product $GA$ acts on the vector space $V$ by linear transformations; and discuss the existence of the regular $A$-module in $V_{_{A}}$.