A generalised quadrangle is a point–line incidence geometry G such that: (i) any two points lie on at most one line, and (ii) given line L point p not incident with L, there unique collinear p. They are specific case of the polygons introduced by Tits (1959), these structures their automorphism groups some importance in finite geometry. An integral part understanding quadrangles knowing which c...

let $g$ be a finite group‎. ‎we denote by $psi(g)$ the integer $sum_{gin g}o(g)$‎, ‎where $o(g)$ denotes the order of $g in g$‎. ‎here we show that‎ ‎$psi(a_5)< psi(g)$ for every non-simple group $g$ of order $60$‎, ‎where $a_5$ is the alternating group of degree $5$‎. ‎also we prove that $psi(psl(2,7))

let l := u3(11). in this article, we classify groups with the same order and degree pattern as an almost simple group related to l. in fact, we prove that l, l:2 and l:3 are od-characterizable, and l:s3 is 5-fold od-characterizable.