The group $J_4 \times J_4$ is recognizable by spectrum

TL;DR

This paper proves that the spectrum of the direct product of two copies of the sporadic simple group J_4 uniquely identifies this group among all finite groups.

Contribution

It establishes the spectral recognizability of the group J_4 × J_4, a significant result in the spectral characterization of finite groups.

Findings

J_4 × J_4 is uniquely determined by its spectrum

The spectrum of J_4 × J_4 distinguishes it from all other finite groups

Spectral recognition applies to this specific product of sporadic groups

Abstract

The spectrum of a finite group is the set of its element orders. In this paper we prove that the direct product of two copies of the finite simple sporadic group $J_4$ is uniquely determined by its spectrum in the class of all finite groups.