Pi-solvable group

Definition
Let $$\pi$$ be a set of primes and $$G$$ be a finite group. Then, $$G$$ is termed a $$\pi$$-solvable group if $$G$$ is a p-solvable group for every prime $$p \in \pi$$.

Every finite group is $$\pi$$-solvable for $$\pi$$ disjoint from the set of prime divisors of $$G$$. In contrast, if $$\pi$$ is the set of prime divisors of $$G$$, $$G$$ is $$\pi$$-solvable if and only if $$G$$ is solvable.

Stronger properties

 * Weaker than::Solvable group

Weaker properties

 * Stronger than::Pi-separable group