A characterization of \mathbf{L_۲(۸۱)} by nse

Let \pi_e(G) be the set of element orders of a finite group G‎. ‎Let nse(G)=\{m_n\mid n\in\pi_e(G)\}‎, ‎where m_n be the number of elements of order n in G‎. ‎In this paper‎, ‎we prove that if nse(G)=nse(L_۲(۸۱))‎, ‎then G\cong L_۲(۸۱)‎.

کلیدواژه ها:

‎set of the numbers of elements of the same order‎ ، ‎order of an element‎ ، ‎Thompson's problem