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Non-injective inductions and restrictions of modules over finite groups

Conghui Li, Yuting Tian

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.

Non-injective inductions and restrictions of modules over finite groups

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.

Paper Structure

This paper contains 3 sections, 10 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Definitions and some lemmas
  3. Proof of the main result

Key Result

Lemma 2.2

Assume $G$ is a finite group, $K\unlhd G$ and denote by $\pi\colon\, G \to G/K$ the natural surjection. Let $V$ be an $RG$-module.

Theorems & Definitions (19)

  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Theorem 3.1: tansitivity
  • Theorem 3.2
  • ...and 9 more