P-dominated group

Definition
A finite group $$G$$ is termed a $$p$$-dominated group for some prime $$p$$ if it satisfies the following conditions:


 * 1) $$G$$ is a defining ingredient::finite complete group: in other words, $$G$$ is complete: it is centerless and every automorphism of the group is inner.
 * 2) The defining ingredient::Fitting subgroup $$F(G)$$ is a $$p$$-group.
 * 3) The quotient $$G/F(G)$$ is a $$p'$$-group (i.e., its order is relatively prime to $$p$$). In fact, $$G$$ is a semidirect product of $$F(G)$$ and a $$p'$$-group.

Facts

 * Every finite group is the Fitting quotient of a p-dominated group for any prime p not dividing its order