# 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