Strongly UL-intersection-closed subgroup property
From Groupprops
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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
Definition
A subgroup property is termed strongly UL-intersection-closed if for any group
, any (possibly empty) indexing set
, and subgroups
, such that
satisfies property
in
for each
, we have:
satisfies property
in
.
A subgroup property is strongly UL-intersection-closed if and only if it is both UL-intersection-closed and identity-true.