Join of subnormal subgroups
From Groupprops
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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 |
Definition
Symbol-free definition
A subgroup of a group is termed a join of subnormal subgroups if it can be expressed as the join of a collection of subnormal subgroups of the group.
Formalisms
In terms of the join-closure operator
This property is obtained by applying the join-closure operator to the property: subnormal subgroup
View other properties obtained by applying the join-closure operator
