Strongly p-solvable group

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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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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:

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

Relation with other properties

Weaker properties


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