Question

Let G be a group of order 39 such that it has exactly one subgroup of order 3 and exactly one subgroup of order 13. Then, which one of the following statements is TRUE ?

• A. G is necessarily cyclic
• B. G is abelian but need not be cyclic
• C. G need not be abelian
• D. G has 13 elements of order 13

Answer 1

Answer: (A)

G is necessarily cyclic

Answer 2

The correct option is (A) : G is necessarily cyclic.