# Nilpotent quotient-by-core subgroup

From Groupprops

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]

This is a variation of normality|Find other variations of normality | Read a survey article on varying normality

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## Definition

### Symbol-free definition

A subgroup of a group is said to be **nilpotent quotient-by-core** if the quotient-by-core of this subgroup (that is, its quotient by its normal core) is a nilpotent group.

### Definition with symbols

A subgroup in a group is termed **nilpotent quotient-by-core** if is a nilpotent group where denotes the normal core of (or the intersection of conjugates of ).

## Relation with other properties

### Stronger properties

- Normal subgroup
- Permutable subgroup (when we are working with finite groups)
- Modular subgroup (when we are working with finite groups)