Question

Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L ≠ G and that the size of L is at least 4. The size of L is _______.

Answer 1

Lagrange’s theorem specifies: Order of subgroup divides the order of a group

order of a group= number of elements in a group = 15

L is a subgroup

L ⊆ G and L ≠ G 

Divisor of 15 = 1, 3, 5, 15

L is at least 4, that is L ≥ 4

The size of L is 5