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 A characterization of some $PGL(2, q)$ by maximum element orders Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 2025-2034 https://doi.org/10.4134/BKMS.2015.52.6.2025Published online November 30, 2015 Jinbao Li, Wujie Shi, and Dapeng Yu Chongqing University of Arts and Sciences, Chongqing University of Arts and Sciences, Chongqing University of Arts and Sciences Abstract : In this paper, we characterize some $PGL(2, q)$ by their orders and maximum element orders. We also prove that$PSL(2, p)$ with $p\geqslant 3$ a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if $q=p^n$ with $p$ a prime and $n>1$, $PGL(2, q)$ can not be uniquely determined by their orders and maximum element orders. Several known results are generalized. Keywords : finite simple groups, maximum element order, characterization MSC numbers : 20D05, 20D45, 20D60 Downloads: Full-text PDF