Join of finitely many subnormal subgroups
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
If the ambient group is a finite group, this property is equivalent to the property: subnormal subgroup
View other properties finitarily equivalent to subnormal subgroup | View other variations of subnormal subgroup |
This is a variation of subnormality|Find other variations of subnormality |
Note that in a group satisfying subnormal join property, being a join of finitely many subnormal subgroups is precisely equivalent to being a subnormal subgroup.
In terms of the finite-join-closure
This property is obtained by applying the finite-join-closure to the property: subnormal subgroup
View other properties obtained by applying the finite-join-closure
Relation with other properties
Intermediate subgroup condition
YES: This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.
ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup condition
ABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition
Suppose are groups such that is the join of finitely many subnormal subgroups in . Then, is the join of finitely many subnormal subgroups in .