3 votes 3 votes $O(G) = 12$ and $G$ is cyclic. The total number of generators possible in $G$ are __________. Mathematical Logic tbb-mathematics-2 numerical-answers + – Bikram asked May 24, 2017 • edited Aug 14, 2019 by Counsellor Bikram 284 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 2 votes 2 votes The number of generators of a cyclic group of order O(G) is the number of positive integers which are co-prime with O(G) and less than O(G) . So in the given question, O(G) = 12. So, positive numbers less than 12 which are co-prime with 12 are 1, 5, 7, 11. So, if 'a' is the generator of the group then a^5, a^7, a^11 are also the generators of the group. So the answer is 4 generators. For detailed discussion : https://math.stackexchange.com/questions/786452/how-to-find-a-generator-of-a-cyclic-group ssinghmy answered Jun 12, 2017 • selected Jan 6, 2018 by srestha ssinghmy comment Share Follow See all 0 reply Please log in or register to add a comment.