Subgroup-closed group property
From Groupprops
This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
View a complete list of group metaproperties
Contents
Definition
Symbol-free definition
A group property is said to be subgroup-closed or S-closed if any subgroup of a group having the property also has the property.
Definition with symbols
A group property is said to be subgroup-closed or S-closed if whenever
satisfies property
and
is a subgroup of
,
must also satisfy property
.