(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cyclic groups

**Physics Forums | Science Articles, Homework Help, Discussion**