Easy# Subgroup of a Group: Subgroup Generated by Elements, Definition

ABSALG-ZYNSDX

Let $G$ be a group, and $S$ be a non-empty subset of $G$.

The subgroup $\langle S\rangle$ of $G$ generated by $S$ is defined as: **the intersection of all subgroups of $G$ containing $S$**, and $S$ is called a **generating set** for $\langle S\rangle$.

The elements of $S$ are called **generators** of $\langle S\rangle$.

Denote:

by $({\mathbb Z}/m{\mathbb Z})^\ast$, $m\ge 2$, the group of reduced (coprime to $m$) residue classes mod $m$.

by ${\mathbb Z}$ the additive group of integers.

by ${\mathbb Q}^\ast$ the multiplicative group of non-zero rational numbers.

Which of the following are **true**?

Select **ALL** that apply.