Tour:Objective evaluator four (beginners)

This objective evaluator is meant as a diagnostic. If you get any of these questions wrong, review the corresponding tour pages and mind's eye tests.

Expect to take about three to five minutes per question.

True/false questions

 * 1) Two cyclic groups are isomorphic if and only if they have the same order.
 * 2) Suppose $$H$$ and $$K$$ are cyclic subgroups of a group $$G$$. Then, the intersection $$H \cap K$$ is also a cyclic subgroup of $$G$$.
 * 3) Suppose $$H$$ and $$K$$ are cyclic subgroups of a group $$G$$. Then, the join $$\langle H, K \rangle$$ is also cyclic.
 * 4) Any group of prime order is cyclic.