let $g$ be an automorphism group of a‎ ‎$2$-$(v,k,4)$ symmetric design $mathcal d$‎. ‎in this paper‎, ‎we‎ ‎prove that if $g$ is flag-transitive point-primitive‎, ‎then the‎ ‎socle of $g$ cannot be an exceptional group of lie type‎.

‎let $g$ be a finite group‎. ‎in [ghasemabadi et al.‎, ‎characterizations of the simple group ${}^2d_n(3)$ by prime graph‎ ‎and spectrum‎, ‎monatsh math.‎, ‎2011] it is‎ ‎proved that if $n$ is odd‎, ‎then ${}^2d _n(3)$ is recognizable by‎ ‎prime graph and also by element orders‎. ‎in this paper we prove‎ ‎that if $n$ is even‎, ‎then $d={}^2d_{n}(3)$ is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎...

We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.

From Cartan and Killing’s original classification of simple Lie groups in the 1890s, these groups have been understood to be of two rather different types: the infinite families of classical groups (related to classical linear algebra and geometry); and a finite number of exceptional groups, ranging from the 14-dimensional groups of typeG2 to the 248-dimensional groups of typeE8. Often it is po...