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The Number of Elements Satisfying g7=e in a finite Group F is ______(a) even(b) not a number(c) odd(d) rationalI got this question in an internship interview.The above asked question is from Cyclic Groups in chapter Groups of Discrete Mathematics

Answer»

The correct answer is (C) ODD

For explanation I would say: LET g≠e be an element in group F such that g7=e. As 7 is a prime number, this yields that the ORDER of g is 7. Consider, the subgroup (g) is generated by g. As the order of g is 7, the order of the subgroup (g)is 7. Hence, the order MUST be odd.



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