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.2015.52.6.2025
Published 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
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