Groups with the same set of orders of maximal abelian subgroups

Abstract

Let $n \geq 3$ be an even number. In this paper, we show how the orders of maximal abelian subgroups of the finite group $G$ can influence on the structure of $G$. More precisely, we show that if for a finite group $G$, $M(G)=M(B_n(q))$, then $G \cong B_n(q)$. Note that $M(G)$ is the set of orders of maximal abelian subgroups of $G$.