An identification theorem for $PSU_6(2)$ and its automorphism groups

TL;DR

This paper establishes a characterization of certain groups related to $PSU_6(2)$ and its automorphisms by analyzing the structure of centralizers of elements of order 3, aiding in their identification.

Contribution

It provides an identification theorem for $PSU_6(2)$ and its automorphism groups based on centralizer structures, which is a new approach in group theory.

Findings

Identifies $PSU_6(2)$ and related groups from centralizer structures.

Provides a method to distinguish these groups using element centralizers.

Enhances understanding of automorphism groups of $PSU_6(2)$.

Abstract

We identify the groups $PSU_6(2)$, $PSU_6(2):2$, $PSU_6(2):3$ and $Aut(PSU_6(2))$ from the structure of the centralizer of an element of order 3.