Direct product-closed subgroup property
From Groupprops
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions
Contents |
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article is about a general term. A list of important particular cases (instances) is available at Category:Direct product-closed subgroup properties
Definition
Definition with symbols
A subgroup property is termed direct product-closed if, given a nonempty indexing set
, and a collection of group-subgroup pairs
for
, such that each
satisfies
as a subgroup of
, then the direct product of the
s satisfies
via its natural embedding in the direct product of
s.