Question

For a cyclic group of order 420 , the number of generators are

Answer 1

Answer:

For b= a s square to be a generator of G, we only require that H generated by b has the same number of elements with G (since H is already a subgroup of G). Hence, we will count the number of different s values such that gcd(s,15)=1,gcd(s,15)=1, which means that the number of generators is equal to the number of numbers that are smaller than 15 and relatively prime to 15. All such numbers are:

1,2,4,7,8,11,13,141,2,4,7,8,11,13,14 (8 of them)

Therefore, there are 8 generators of a cyclic group of order 15.