P-dominated group

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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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 finite complete group: in other words, $G$ is complete: it is centerless and every automorphism of the group is inner.
2. The 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