Unitary t-groups

TL;DR

This paper classifies all unitary t-groups for t ≥ 2 across all dimensions and identifies the unique properties of the unitary 4-group, including its relation to higher t-groups.

Contribution

It provides a comprehensive classification of unitary t-groups for t ≥ 2 and establishes the uniqueness of the unitary 4-group in this context.

Findings

Complete classification of unitary t-groups for t ≥ 2

Identification of the unique unitary 4-group

Demonstration that the 4-group is also a 5-group but not for t ≥ 6

Abstract

Relying on the main results of [Guralnick-Tiep], we classify all unitary $t$-groups for $t \geq 2$ in any dimension $d \geq 2$. We also show that there is essentially a unique unitary $4$-group, which is also a unitary $5$-group, but not a unitary $t$-group for any $t \geq 6$.