2. Subgroups and Cyclic Groups

Subgroup Tests — Quiz

Test your understanding of subgroup tests with 5 practice questions.

Practice Questions

Question 1

Which condition is a sufficient subgroup test for a nonempty subset $H$ of a group $G$?

Question 2

In an additive group, which condition is the standard subgroup test for a nonempty subset $H$?

Question 3

Which subset of $(\mathbb{Z},+)$ is a subgroup?

Question 4

Which subset of $(\mathbb{R},+)$ is not a subgroup?

Question 5

Let $H=\{3k:k\in\mathbb{Z}\}$ inside $(\mathbb{Z},+)$. Which calculation best shows that $H$ satisfies the subgroup test?