On the NSE characterization of certain finite simple groups

For a group G, \pi_e(G) and s_m(G) are denoted the set of orders of elements and the number of elements of order m in G, respectively. Let {\rm nse}(G)=\{s_m(G) \ | \ m\in \pi_e(G)\}. An arbitrary finite group M is NSE characterization if, for every group G, the equality {\rm nse}(G)={\rm nse}(M) implies that G\cong M. In this paper, we are going to show that the non-Abelian finite simple groups A_۹, A_{۱۰}, A_{۱۲}, U_۴(۳), U_۵(۲), U_۶(۲), S_۶(۲), O_۸^+(۲) and HS are characterizable by NSE.

کلیدواژه ها:

Element order ، finite simple group ، Prime graph