Subgroup intersection restriction expression

This page describes a formal expression, or formalism, that can be used to describe certain subgroup properties.

View a complete list of formal expressions for subgroup properties OR [[:Category:{{{1}}}|View subgroup properties expressible using this formalism]]

Definition

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 $H\leq G$ satisfies proeprty $p\to q$ if for any subgroup $K$ satisfying property $p$ in $G$, $H\cap K$ satisfies $q$ in $H$.