Join of subnormal subgroups

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Join of subnormal subgroups, all facts related to Join of subnormal subgroups) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

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]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

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

Relation with other properties

Stronger properties

• Normal subgroup
• Subnormal subgroup
• Join of finitely many subnormal subgroups

Weaker properties

• Subnormal automorphism-invariant subgroup