Is Zopf4Zopf times Zopf6Zopf isomorphic to Zopf24Zopf Is Zop

Is Zopf/4Zopf times Zopf/6Zopf isomorphic to Zopf/24Zopf? Is Zopf/4Zopf times Zopf/5Zopf isomorphic to Zopf/20Zopf?

Solution

Z/4Z × Z/6Z is not isomorphic to Z/24Z.

there is a theorem says, Z/mZ × Z/nZ is isomorphic to Z/mnZ if and only if m and n are relatively prime. (GCD(m,n)=1)

Using same theorem,

Z/4Z × Z/5Z is isomorphic to Z/20Z

As 4 and 5 are relatively prime.