The Number of Elements Satisfying g7=e in a finite Group F is ______
A. even
B. not a number
C. odd
D. rational
Answer:C
The Number of Elements Satisfying g7=e in a finite Group F is ______
A. even B. not a number C. odd D. rational
Explanation: 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.