A characterization of some $PGL(2, q)$ by maximum element orders

摘要

In this paper, we characterize some $PGL(2, q)$ by their orders and maximum element orders. We also prove that$PSL(2, p)$ with $pgeqslant 3$ 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.