GATE | GATE-CS-2014-(Set-3) | Question 65

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 __________.
(A) 3
(B) 5
(C) 7
(D) 9


Answer: (B)

Explanation: This is according to Lagrange’s theorem that states that the order of subgroup should divide the order of group. Subgroups of G can be of order 1,3,5 or 15 and according to the conditions and choices, B is the right answer.

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