Hey I've been working on this question,(adsbygoogle = window.adsbygoogle || []).push({});

How that the following is a homomorphism

[tex]\theta :{{D}_{2n}}\to {{D}_{2n}}\,\,\,givenby\,\,\,\theta ({{a}^{j}}{{b}^{k}})={{b}^{k}}\,\,\,[/tex]

[tex]\theta ({{a}^{j}}{{b}^{k}})\theta ({{a}^{m}}{{b}^{n}})={{b}^{k}}{{b}^{n}}[/tex]

[tex]\theta ({{a}^{j}}{{b}^{k}}{{a}^{m}}{{b}^{n}})=?[/tex]

From what it looks like it isn't a homomorphism but I'm not sure how to evaluate the last line,

Does anyone know how to evaluate it?

I also have another question which I solved numerically but I'm not sure how to show it algebraically,

Would anyone know how to show

[tex]\text{Remaider}\left( \frac{ab}{n} \right)\ne \text{Remainder}\left( \frac{a}{n} \right)\times \text{Remainder}\left( \frac{b}{n} \right) For\,\,a,b,n\in \mathbb{Z}[/tex]

Or would it be sufficient to just know that its not true?

**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!

# Homework Help: Group homomorphism problem

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