OD-Characterization of Some Simple Unitary Groups

TL;DR

This paper investigates the OD-characterization of simple unitary groups, demonstrating that certain groups like U_3(q) and U_4(q) are uniquely identified by their order and degree pattern for prime powers less than 100.

Contribution

It proves the OD-characterization for specific simple unitary groups, expanding understanding of their uniqueness based on degree patterns.

Findings

U_3(q) and U_4(q) are OD-characterizable for q<100

The degree pattern uniquely determines these groups among finite groups

The study advances classification of simple unitary groups by degree pattern

Abstract

The degree pattern of a finite group is the degree sequence of its prime graph in ascending order of vertices. We say that the problem of OD-characterization is solved for a finite group if we determine the number of pairwise nonisomorphic finite groups with the same order and degree pattern as the group under consideration. In this article the problem of OD-characterization is solved for some simple unitary groups. It was shown, in particular, that the simple unitary groups $U_3(q)$ and $U_4(q)$ are OD-characterizable, where $q$ is a prime power $<10^2$.