Subgroup of prime characteristic

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

A subgroup $H$ of a group $G$ is said to be of characteristic $p$ for a prime $p$ if $H$ is a $p$-local subgroup of $G$ such that $C_{H}(O_{p}(H))$ is contained in $O_{p}(H)$.