Tour:Objective evaluator four (beginners)

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This page is a Objective evaluator page, part of the Groupprops guided tour for beginners (Jump to beginning of tour)
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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.