2. Subgroups and Cyclic Groups

Generated Subgroups — Quiz

Test your understanding of generated subgroups with 5 practice questions.

Practice Questions

Question 1

In multiplicative notation, what is the subgroup generated by an element $a$ in a group $G$?

Question 2

In the additive group $\mathbb{Z}$, what is the subgroup generated by $4$?

Question 3

In the additive group $\mathbb{Z}_{10}$, what is $\langle 5\rangle$?

Question 4

Which statement best describes the notation $\langle S\rangle$ for a subset $S$ of a group?

Question 5

What is the subgroup generated by the empty set in a group?