Repeat Exercise 47 for the general situation of the set H of all solutions x of the equation xⁿ = e for a fixed integer n ≥ 1 in an abelian group G with identity e.

Data from exercise 47

Prove that if G is an abelian group, written multiplicatively, with identity element e, then all elements x of G satisfying the equation x² = e form a subgroup H of G.