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A note on blocks of finite groups with TI Sylow $p$-subgroups

Deniz Yılmaz

Abstract

Let $\mathbb{F}$ be an algebraically closed field of characteristic zero. Recently, we proved that isotypic blocks are functorially equivalent over $\mathbb{F}$. In this article we provide an example of functorially equivalent blocks which are not perfectly isometric.

A note on blocks of finite groups with TI Sylow $p$-subgroups

Abstract

Let be an algebraically closed field of characteristic zero. Recently, we proved that isotypic blocks are functorially equivalent over . In this article we provide an example of functorially equivalent blocks which are not perfectly isometric.
Paper Structure (2 theorems)

This paper contains 2 theorems.

Key Result

Theorem 1

Let $G$ be a finite group with TI Sylow $p$-subgroup $P$. Let $b$ be a block idempotent of $kG$ with a defect group $P$ and let $c$ be the block idempotent of $kN_G(P)$ which is in Brauer correspondence with $b$. Then the pairs $(G,b)$ and $(N_G(P),c)$ are functorially equivalent over $\mathbb{F}$.

Theorems & Definitions (2)

  • Theorem 1
  • Corollary 2