Subgroup intersection restriction expression

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