Moderate# Normal Subgroup: Definition, Examples Abelian, Cyclic Subgroups

ABSALG-NLYZO8

Let $G$ be a group with neutral element $e$.

A normal subgroup $N$ of $G$, written $N\vartriangleleft G$, is a subgroup such that $gN=Ng$, for all $g\in G$.

The **center** of a group is the set of elements of $G$ that commute with every element of $G$.

A **cyclic group** is a group consisting of all powers $g^n$, $n\in\mathbb{Z}$, of a single element $g$.

Which of the following are **false** in general?

Select **ALL** that apply.