let p be a prime number. if a group G has more than p-1 elements of order p, prove that G cannot be a cyclic group?

kokomocutie88r1

kokomocutie88r1

Answered question

2022-07-28

let p be a prime number. if a group G has more than p-1 elements of order p, prove that G cannot be a cyclic group?

Answer & Explanation

dtal50

dtal50

Beginner2022-07-29Added 10 answers

If G is a cyclic group of order n , then for any divisor d of n there exists exactly one unique subgroup of G of order d , which is also cyclic .
A cyclic group of order m has ?(m) different generators , with ?= the totient function of Euler.
For any prime
?(p) = p-1.

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