Groups With the Same Set of Orders of Maximal Abelian Subgroups


Neda Ahanjideh, Ali Iranmanesh




Let $n>3$ 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 $G$. Let $\Gamma(G)$ denote the non-commuting graph of $G$. As a consequence of our result, we show that if $G$ is a finite group with $\Gamma(G)\cong(B_n(q))$, then $G\cong B_n(q)$.