A note on the Triple Product Property subgroup capacity of finite groups

TL;DR

This paper presents a new, sharper upper bound for the TPP subgroup capacity of finite groups, which is relevant for improving bounds on the matrix multiplication exponent.

Contribution

It introduces a novel upper bound for the TPP subgroup capacity, enhancing previous theoretical limits in the context of group-theoretic matrix multiplication.

Findings

New upper bound for TPP subgroup capacity

Implications for bounds on matrix multiplication exponent

Refinement of theoretical limits in group-theoretic methods

Abstract

In the context of group-theoretic fast matrix multiplication the TPP capacity is used to bound the exponent $\omega$ of matrix multiplication. We prove a new and sharper upper bound for the TPP subgroup capacity of a finite group