A solvable group isospectral to S(4,3)

TL;DR

This paper constructs a specific solvable group that shares the same element order spectrum as the simple group S(4,3), advancing the understanding of group spectra and their relation to group structure.

Contribution

It provides the first explicit example of a solvable group with the same element orders as a particular simple group, completing the classification of simple groups with solvable isospectral counterparts.

Findings

Constructed a solvable group of order 5648590729620 with the same spectrum as S(4,3)

Confirmed the complete classification of finite simple groups with solvable isospectral groups

Abstract

We construct a solvable group G of order 5648590729620 such that the set of element orders of G coincides with that of the simple group S(4,3). This completes the determination of finite simple groups isospectral to solvable groups.