Sur le centralisateur d'une involution de 2E6(2)

TL;DR

This paper proves that the centralizer of an involution in the group 2E6(2) is a quotient of a Coxeter group, providing a presentation that resolves a long-standing open problem in group theory.

Contribution

It establishes that the centralizer 2^{20+1}.U_6(2) is a quotient of a Coxeter group and offers a new presentation as a Q_{222}-group, solving a long-standing question.

Findings

Proves the centralizer is a quotient of a Coxeter group.

Provides a presentation of the centralizer as a Q_{222}-group.

Resolves a long-standing open problem in the structure of 2E6(2).

Abstract

In this paper we prove that $2^{20+1}.U_6(2)$, known as the centralizer of an involution in the group $2E_6(2)$ is a quotient of a Coxeter group. We obtain a presentation of $2^{20+1}.U_6(2)$ as a $Q_{222}$-group, which now resolve a long pending question.