Characterization of $\mathbf{L_2(p^2)}$ by NSE

Subject Areas : International Journal of Industrial Mathematics

H. Parvizi ‎Mosaed‎‎ ¹ , A. Tehranian ²

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Received: 2015-07-05 Accepted : 2015-07-05 Published : 2015-07-01

Keywords: Element order, The set of the number of eleme, Simple $K_n$-group, Projective special linear ‎gro,

Abstract :

Let $G$ be a group and $\pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $nse(G)$ be the set of the number of elements of the same order in $G$. In this paper, we prove that the simple group $L_2(p^2)$ is uniquely determined by $nse(L_2(p^2))$, where $p\in\{11,13\}$‎.‎