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**

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 and isomorphisms

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