Strongly p-solvable group

Definition
Let $$G$$ be a finite group and $$p$$ be an odd prime number. We say that $$G$$ is strongly $$p$$-solvable if it satisfies both the following conditions:


 * $$G$$ is a defining ingredient::p-solvable group.
 * Either $$p \ge 5$$ or $$p = 3$$ and no subquotient of $$G$$ is isomorphic to defining ingredient::special linear group:SL(2,3).

Note that for $$p = 2$$, there is no notion of strong solvability.

Weaker properties

 * Stronger than::p-solvable group:
 * Stronger than::p-constrained group:
 * Stronger than::p-stable group: