Parabolic subgroup for a prime

The article defines a subgroup property, where the definition may be in terms of a particular prime number that serves as parameter
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Definition

Definition with symbols

Given a finite group $G$ and a prime $p$, a subgroup $H$ of $G$ is said to be $p$-parabolic if it satisfies the following condition: let $P=O_{p}(H)$, that is, the Sylow core (largest normal $p$-subgroup) of $H$. Then, $H=N_{G}(P)$.

Relation with other properties

Stronger properties

• Sylow normalizer