Transfer condition operator

This article defines a subgroup property modifier (a unary subgroup property operator) -- viz an operator that takes as input a subgroup property and outputs a subgroup property

View a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)

Definition

Suppose $p$ is a subgroup property. The transfer condition operator applied to $p$, denoted $T(p)$, is defined as the following property: a subgroup $H$ of a group $G$ satisfies $T(p)$ if, for any subgroup $K$ of $G$, $H\cap K$ satisfies property $p$ in $K$.