Bulletin of the
Korean Mathematical Society BKMS

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