1,004 views
1 votes
1 votes
The order of cyclic group is equal to order of generating element....

 

 

Somebody explain with example plz

2 Answers

0 votes
0 votes
It can or cannot be. Because the order of group should be divisible by the order of element.
0 votes
0 votes
Yes it has to be !  Because if the order of an element is equal to order of the group then such an element will surely be the generator because order of an element says the periodicity. For an element to be called as generator, its periodicity should be order of group, otherwise all elements can't be generated

Related questions

5 votes
5 votes
1 answer
1
Lakshman Bhaiya asked Oct 7, 2018
2,115 views
Suppose that $G$ is a cyclic group of order $10$ with generator $a\in G$.Order of $a^{8}$ is _______
1 votes
1 votes
1 answer
2
bts1jimin asked Jan 21, 2019
445 views
1-) 12-) 23-) 34-) 4
1 votes
1 votes
1 answer
3
ankitgupta.1729 asked Dec 6, 2017
1,137 views
Find all the subgroups of a cyclic group of order 12.(A) {e},(a6),(a4),(a3),(a2),(a)(B) (a12),(a6),(a4),(a3),(a2),(a)(C) (a12),(a6),(a4),(a2),(a)(D) (a12),(a6),(a4),(a3),...
2 votes
2 votes
2 answers
4
Rahul_Rathod_ asked Jan 16, 2019
1,449 views
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___