- #1

hsong9

- 80

- 1

## Homework Statement

Let G and H be cyclic groups, with |G| = m and |H| = n. If gcd(m,n) =1, show that G x H is cyclic.

## The Attempt at a Solution

Let a = (g,h) in G x H. Then |a| = lcm (|g|,|h|).

Since gcd(m,n)=1, then lcm (m,n) = mn.

Thus lcm (|g|,|h|) = lcm (m,n) = mn.

so <a> = G x H has mn elements and a cyclic group.

Right?