# Math Help - Isomorphic problem

1. ## Isomorphic problem

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 $\mathbb{Z}_8$.*

*)A classic result is that the multiplicative group of a finite field must be cyclic. That is the only cyclic group on that list.