Finite-upper join-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
Definition
A subgroup property is termed a finite-upper join-closed subgroup property if, for any subgroup
of a group
, and any intermediate subgroups
of
such that
satisfies
in both
and
, we have that
satisfies
in the join of subgroups
.