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GATE 2014 [Set-3]
April 4, 2025GATE 2014 [Set-3]
April 4, 2025GATE 2014 [Set-3]
| Question 13 |
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 __________.
| 5 | |
| 6 | |
| 7 | |
| 8 |
Question 13 Explanation:
Lagrange’s theorem, in the mathematics of group theory, states that for any finite group G, the
order (number of elements) of every subgroup H of G divides the order of G.
So, 15 is divided by {1, 3, 5, 15}.
As minimum is 4 and total is 15, we eliminate 1,3,15.
Answer is 5.
order (number of elements) of every subgroup H of G divides the order of G.
So, 15 is divided by {1, 3, 5, 15}.
As minimum is 4 and total is 15, we eliminate 1,3,15.
Answer is 5.
Correct Answer: A
Question 13 Explanation:
Lagrange’s theorem, in the mathematics of group theory, states that for any finite group G, the
order (number of elements) of every subgroup H of G divides the order of G.
So, 15 is divided by {1, 3, 5, 15}.
As minimum is 4 and total is 15, we eliminate 1,3,15.
Answer is 5.
order (number of elements) of every subgroup H of G divides the order of G.
So, 15 is divided by {1, 3, 5, 15}.
As minimum is 4 and total is 15, we eliminate 1,3,15.
Answer is 5.