0 votes 0 votes A cyclic group O(G)=200 g be its generator O(g^x)=100 for some x.what is value of x? a.1 b.2 c.3 d.4 1 and 3 cant be possible as [order of generator equal to order of group] how to choose bw 2 and 4??? Abhisek Tiwari 4 asked Jan 21, 2019 Abhisek Tiwari 4 381 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Formulae for the order of generator for a cyclic group is: O(g^x) = O(G) / [ GCD(O(G) , x) ] In the given question, x=? , O(G) = 200, O(g^x) = 100. 100 = 200 / GCD(200, x) --> GCD(200,x) = 2 --> x = 2. So the O(g^x) = 2. balchandar reddy san answered Jan 21, 2019 balchandar reddy san comment Share Follow See all 3 Comments See all 3 3 Comments reply Abhisek Tiwari 4 commented Jan 21, 2019 reply Follow Share how this formula came?Any Ref 0 votes 0 votes balchandar reddy san commented Jan 21, 2019 reply Follow Share Assume there are 6 elements in a cyclic group {a^0,a^1,a^2,a^3,a^4,a^5}. Here, all elements are generators. let's find O[(a^1)^2], it will generate {a^2,a^4,a^0,a^2,a^4....} set of elements with order 3.. which is 6/GCD(6,2). let me know if anything is unclear.. 0 votes 0 votes Shaik Masthan commented Jan 31, 2019 reply Follow Share @Abhisek Tiwari 4 https://gateoverflow.in/250931/cyclic-group 0 votes 0 votes Please log in or register to add a comment.