Nilpotent implies center is normality-large

This article gives the statement, and possibly proof, of the fact that in any nilpotent group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) always satisfies a particular subgroup property (i.e., normality-large subgroup)
View all such subgroup property satisfactions OR View more information on subgroup-defining functions in nilpotent groups

Statement

Verbal statement

In a nilpotent group, the center is a normality-large subgroup; in other words, the intersection of the center with any nontrivial normal subgroup is a nontrivial normal subgroup.

Proof

PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.