Strongly p-solvable 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

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

• $G$ is a p-solvable group.
• Either $p\geq 5$ or no subquotient of $G$ is isomorphic to the group $SL(2,3)$.

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

References

Textbook references

• Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 234, Chapter 6 (Solvable and pi-solvable groups), Section 6.5 (p-stability in p-solvable groups), ^{More info}