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On p-permutation equivalences between direct products of blocks

Deniz Yılmaz

Abstract

We extend the notion of a p-permutation equivalence to an equivalence between direct products of block algebras. We prove that a p-permutation equivalence between direct products of blocks gives a bijection between the factors and induces a p-permutation equivalence between corresponding blocks.

On p-permutation equivalences between direct products of blocks

Abstract

We extend the notion of a p-permutation equivalence to an equivalence between direct products of block algebras. We prove that a p-permutation equivalence between direct products of blocks gives a bijection between the factors and induces a p-permutation equivalence between corresponding blocks.
Paper Structure (2 sections, 5 theorems, 19 equations)

This paper contains 2 sections, 5 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. The proof of the main theorem

Key Result

Theorem 1.3

Let $G_1,\cdots,G_n$ and $H_1,\cdots,H_m$ be finite groups. Let $A_i\in\mathrm{Bl}(\mathcal{O} G_i)$ and $B_j\in\mathrm{Bl}(\mathcal{O} H_j)$ be block algebras for $i=1,\cdots, n$ and $j=1,\cdots,m$. Assume that $\mathcal{O}$ contains a root of unity of order the exponent of $G_i$ and $H_j$ for each

Theorems & Definitions (8)

  • Definition 1.1
  • Definition 1.2
  • Theorem 1.3
  • Proposition 2.4
  • Corollary 2.5
  • Proposition 2.6
  • Remark 2.7
  • Corollary 2.8