If G is a cyclic group and a ∈ G is a generator -VirtualGATE-17

If G is a cyclic group and a ∈ G is a generator, then

(A) O(G) = O(a)
(B) O(G) > O(a)
(C) O(G) < O(a)
(A) None

Answer

Answer: A

Discuss here.

3Comments
Hradesh @hradeshpatel
11 Aug 2016 12:52 am

 what is B?????????

techtud official @techtud
14 Aug 2016 09:58 am

That was a typo, it should be G.

Habib Mohammad Khan @habibkhan
11 Aug 2016 04:46 pm

Ya it should be G instead of B.It is a well known theorem that if a cyclic group is finite then ∃ atl least 1 element x such that order(x) = order(group)