Inertial 2-blocks with abelian defect groups

TL;DR

This paper proves that 2-blocks with certain abelian defect groups are inertial, expanding the class of known inertial blocks in modular representation theory.

Contribution

It establishes that 2-blocks with defect groups as specified products of cyclic 2-groups are inertial, a significant result in the theory of blocks with abelian defect groups.

Findings

2-blocks with defect groups $C_{2^{n_1}} imes ... imes C_{2^{n_t}}$ are inertial

The result applies when all $n_i \\geq 2$

Advances understanding of inertial blocks with abelian defect groups

Abstract

L. Puig defined inertial blocks. In this paper, we prove that 2-blocks with defect group $C_{2^{n_1}}\times C_{2^{n_2}}\times...\times C_{2^{n_t}}$ are inertial, where $n_i\geq 2$ for all $i$.