IIT Kanpur

Question

5. Which of the following is correct for a finite group?
    A. The order of an element is always equal to the order of the group.
    B. The order of an element is always less or equal to the order of the group.
    C. The order of an element divides the order of the group.
    D. None of the above

Comments

Ans is B

Answer 1

B and C. Both are correct.

C is correct because of Langrage's theorem. Correctness of C implies Correctness of B.

Comments

I think C) will be ans directly from lagrange's theorem

less than and equal to doesnot mean, it will be always disible by order of group

right?

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See, The Statement of option C is NOT wrong. To make it wrong, You'd have to give at least one case where Order of an Element is Greater than Order of the Group. That is why I said "Correctness of C implies Correctness of B" , Not the vice versa. This is One way (Implication).