Bull. Korean Math. Soc. 2015; 52(6): 2025-2034
Printed November 30, 2015
https://doi.org/10.4134/BKMS.2015.52.6.2025
Copyright © The Korean Mathematical Society.
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
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
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