Thread: cyclic group

i need a clue to prove this. can any one please help?
If a & b be elements of a group G, & o(a)=m (read order of a= m) and o(b)= n and gcd(m,n)=1
then <a> (intersection) <b>= {identity}

Originally Posted by srv123

i need a clue to prove this. can any one please help?
If a & b be elements of a group G, & o(a)=m (read order of a= m) and o(b)= n and gcd(m,n)=1
then <a> (intersection) <b>= {identity}

Welcome to MHF, srv123!

Suppose the intersection is not empty.
That means there must be an element c=a^i=b^j with i<m and j<n.
Can you draw any conclusions about this element (leading to a contradiction)?

thanks...
i get it...o(c) must divide both m and n but they are co-prime...
thanks again..
had a good experience on the 1st day

You're welcome!