# Subgroup intersection restriction expression

A subgroup intersection restriction expression is an expression of a subgroup property in terms of two subgroup properties. The subgroup intersection restriction expression corresponding to subgroup properties $p$ and $q$ is denoted as:
$p \to q$
and is defined as follows: a subgroup $H \le G$ satisfies proeprty $p \to q$ if for any subgroup $K$ satisfying property $p$ in $G$, $H \cap K$ satisfies $q$ in $H$.