# NSCFN-subgroup

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]

## Definition

### Symbol-free definition

A subgroup of a group is termed a **NSCFN-subgroup** if it is normal, fully normalized and self-centralizing in the whole group.

### Definition with symbols

A subgroup of a group is termed a **NSCFN-subgroup** if , is fully normalized in , and .

Equivalently, is a NSCFN-subgroup of if is a normal subgroup of , and the induced homomorphism induced by the conjugation action is surjective with kernel equal to .