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

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Standard XII

Mathematics

Evaluation of a Determinant

Let G be a gr...

Question

Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L $\neq$ G and that the size of L is at least 4. The size of L is ___
5

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Solution

The correct option is A 5
Order of subgroup divides order of gr. (Lagrange's theorem). So order of L has to be 3, 5 or 15. As it is given that the subgroup at least 4 elements and it is not equal to the group, therefore the order of subgroup cant 3 or 15.
Hence it is 5.

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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

The correct option is A 5Order of subgroup divides order of gr. (Lagrange's theorem). So order of L has to be 3, 5 or 15. As it is given that the subgroup at least 4 elements and it is not equal to the group, therefore the order of subgroup cant 3 or 15. Hence it is 5.

Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L $\neq$ G and that the size of L is at least 4. The size of L is ___
5

The correct option is A 5
Order of subgroup divides order of gr. (Lagrange's theorem). So order of L has to be 3, 5 or 15. As it is given that the subgroup at least 4 elements and it is not equal to the group, therefore the order of subgroup cant 3 or 15.
Hence it is 5.