Non-injective inductions and restrictions of modules over finite groups

TL;DR

This paper extends the classical induction and restriction of modules over finite groups to non-injective homomorphisms, establishing key properties like transitivity, Frobenius reciprocity, and Mackey's formula.

Contribution

It introduces a framework for module induction and restriction via non-injective homomorphisms, broadening the scope of representation theory techniques.

Findings

Established transitivity for non-injective inductions and restrictions

Proved Frobenius reciprocity in the non-injective setting

Derived Mackey's formula for non-injective homomorphisms

Abstract

In this note, we extend the inductions and restrictions of modules over finite groups to non-injective group homomorphisms, establishing transitivity, Frobenius reciprocity, Mackey's formula, etc.