TY - JOUR ID - 1058 TI - NSE characterization of some linear groups JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Ahanjideh, N. AU - Mousavi, L. AU - Taeri, B. AD - Faculty of Mathematical Sciences‎, ‎Department of Pure Mathematics‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎Iran. AD - Department of Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan 84156-83111‎, ‎Iran‎. Y1 - 2017 PY - 2017 VL - 43 IS - 5 SP - 1531 EP - 1542 KW - Set of the numbers of elements of the same order‎ KW - ‎prime graph‎ KW - ‎Mersenne number‎ DO - N2 - ‎For a finite group $G$‎, ‎let $nse(G)=\{m_k\mid k\in\pi_e(G)\}$‎, ‎where $m_k$ is the number of elements of order $k$ in $G$‎ ‎and $\pi_{e}(G)$ is the set of element orders of $G$‎. ‎In this paper‎, ‎we prove that $G\cong L_m(2)$ if and only if $p\mid |G|$ and $nse(G)=nse(L_m(2))$‎, ‎where $m\in \{n,n+1\}$ and $2^n-1=p$ is a prime number. UR - http://bims.iranjournals.ir/article_1058.html L1 - http://bims.iranjournals.ir/article_1058_2c5b6c17ba5cdd918988ed6c7b89c0df.pdf ER -