0 votes 0 votes Consider the following statements: S1: Every cyclic group is Abelian group. S2: Every Abelian group is cyclic group. S3: Cyclic group of order 10 have 4 generators. Which of the following is true? Kaluti asked Feb 1, 2018 Kaluti 1.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes s1 is true s2 is false s3 is true Raveena Yadav 1 answered Feb 1, 2018 Raveena Yadav 1 comment Share Follow See all 4 Comments See all 4 4 Comments reply akshat sharma commented Feb 1, 2018 reply Follow Share S3 is true 10 has 4 generator 10=2*5 phi(10)=1*4 phi(5)=5^1-5^0 =4 phi(2)=1 1 votes 1 votes Raveena Yadav 1 commented Feb 1, 2018 reply Follow Share thanks @akshat sharma actually i thought there is only one statement true 1 votes 1 votes `JEET commented Dec 24, 2018 reply Follow Share @akshat sharma How you have applied the above things. I do not really get. For finding the number of generators of the cyclic group, I know that we need to find the number of prime factors but what's after that? 0 votes 0 votes Gate Fever commented Dec 25, 2018 reply Follow Share this is the theorem @`JEET if a cyclic group Gis generated by an element a of order n,then $a^{m}$ is a generator of G if and only if the greatest common divisor of m and n is 1 that is m & n are relatively prime cyclic group of order 10 now in this 1,3,7,9 are the nos which are relatively prime to 10 hence 4 generators!! 1 votes 1 votes Please log in or register to add a comment.