I have a question where it says prove that [itex] G \cong C_3 \times C_5 [/itex] when G has order 15.(adsbygoogle = window.adsbygoogle || []).push({});

And I assumed that as 3 and 5 are co-prime then [itex] C_{15} \cong C_3 \times C_5 [/itex], which would mean that [itex] G \cong C_{15} [/itex]?

So every group of order 15 is isomorohic to a cyclic group of order 15?

Doesn't seem right?

Help would be appreciated! Thanks!

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

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

# Cyclic groups and isomorphisms

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