A group G is expressed as the internal direct product of its subgroups H1, H2, ..., Hn if and only if every element g ∈ G can be uniquely expressed in which form (where hi ∈ Hi)?

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?