Local 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

Symbol-free definition

Let $p$ be a prime. A subgroup of a group is said to be a $p$-local subgroup if it occurs as the normalizer of a $p$-subgroup.

Definition with symbols

Let $p$ be a prime. A subgroup $H$ of a group $G$ is said to be a $p$-local subgroup if there exists a $p$-subgroup $Q$ such that $H=N_{G}(Q)$.

Relation with other properties

Stronger properties

• Local subgroup

Weaker properties

• Sylow-normalizer