# Basic Isomorphic Systems

• May 31st 2010, 03:44 PM
jameselmore91
Basic Isomorphic Systems
I had some trouble with this problem:

Is \$\displaystyle <J_{4}, +_{4}>\$ isomorphic to \$\displaystyle <\${\$\displaystyle 1,-1,i,-i\$}\$\displaystyle , *>\$?

I made product tables but I'm having a hard time identifying the isomorphic relationship. Is there one?
• May 31st 2010, 06:09 PM
tonio
Quote:

Originally Posted by jameselmore91
I had some trouble with this problem:

Is \$\displaystyle <J_{4}, +_{4}>\$ isomorphic to \$\displaystyle <\${\$\displaystyle 1,-1,i,-i\$}\$\displaystyle , *>\$?

I made product tables but I'm having a hard time identifying the isomorphic relationship. Is there one?

If I understand correctly your symbols, we have two cyclic groups of order 4, one written additively (addition modulo 4) and the other one written multiplicatively (complex multiplication). Identify a generator in each and define a map between these two generators, mapping powers of one to powers (or multiples) of the other...

Tonio