In this paper we define S algebras and show that every finite group can be found in some S algebra.  We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.

for $q in {7,8,9,11,13,16}$, we consider the primitive actions of $l_2(q)$ and use key-moori method 1 as described in [codes, designs and graphs from the janko groups {$j_1$} and{$j_2$}, {em j. combin. math. combin. comput.}, {bf 40} (2002) 143--159., correction to: ``codes, designs and graphs from the janko groups{$j_1$} and {$j_2$}'' [j. combin. math. combin. comput. {bf 40} (2002) 143--159],...

Let l be a prime, and let Γ be a finite subgroup of GLn(Fl) = GL(V ). With these assumptions we say that Condition (C) holds if for every irreducible Γ-submodule W ⊂ ad V there exists an element g ∈ Γ with an eigenvalue α such that tr eg,αW 6= 0. Here, eg,α denotes the projection to the generalised α-eigenspace of g. This condition arises in the definition of adequacy in section 2. Let Γ denote...