A UNIFORM CHARACTERIZATION OF THE OCTONIONS AND THE QUATERNIONS USING COMMUTATORS.

Let G be a finite group and C(G) denote the set of all non-normal non-cyclic subgroups of G. In this paper, the function δc(G) = 1 |G| P H∈C(G) |H| is introduced. In fact, we prove that, if δc(G) ≤ 10/3, then either G ∼=A5, or G is solvable. We also find some examples of finite groups G with δc(G) ≤ 10/3. [ABSTRACT FROM AUTHOR]