# Isomorphic problem

• November 8th 2007, 05:57 PM
The nonzero elements of $Z_{3}[i]$ form an Abelian group of order 8 under multiplication. Is it isomorphic to $Z_{8}, Z_{4} \oplus Z_{2}, Z_{2} \oplus Z_{2} \oplus Z_{2}$?
The nonzero elements of $Z_{3}[i]$ form an Abelian group of order 8 under multiplication. Is it isomorphic to $Z_{8}, Z_{4} \oplus Z_{2}, Z_{2} \oplus Z_{2} \oplus Z_{2}$?
It is $\mathbb{Z}_8$.*