Abelian coverings of finite general linear groups and an application to their non-commuting graph

A. Azad, M. A. Iranmanesh, C. E. Praeger +1

In this paper we introduce and study a family ${\mathcal{A}}_n(q)$ of abelian subgroups of $\GL_n(q)$ covering every element of $\GL_n(q)$. We show that ${\mathcal{A}}_n(q)$ contains a…