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## Homework Statement

Explain why Z4 x Z4 is not isomorphic to Z16.

## Homework Equations

Going to talk about units in a ring.

Units are properties preserved by isomorphism.

## The Attempt at a Solution

We see the only units in Z4 are 1 and 3.

So the units of Z4 x Z4 are (1,1) , (3,3) , (1,3) , (3,1)

The Units of Z16 are 1,3,5,7,9,11,13,15.

So there are 4 units in Z4 x Z4 but in Z16 we have 8 units. So there can not be an isomorphism between the two.

Is this correct?