Let p be a prime number. Let G be a group such that for each g ∈ G there exists an n ∈ &mathbb;N; such that gpn = 1. Which of the following statements is FALSE?

In standard notation, what is the order of the subgroup ⟨5⟩ ⊕ ⟨3⟩ in the direct sum group Z30 ⊕ Z12?

If G is a non-cyclic group of order 57, then what is the number of elements of order 3 in G?

Let G be a group of order 29. Which of the following statements is true?