# Homework Help: Isomorphism question

1. May 31, 2010

### tyrannosaurus

1. The problem statement, all variables and given/known data

Prove that Z2+Dn and D2n are not isomorphic whenever n is even by using structural characteristics that demonstrate Z2+Dn and D2n cannot be isomorphic.

2. Relevant equations

3. The attempt at a solution
We know that D2n has 2n+1 order 2 elements, since n is even we know that Dn has n+1 elements of order 2. Thus Z2+Dn has 2(n+1)= 2n+2 order 2 elements. Thus Z2+Dn and D2n are not isomorphic whenever n is even. Is this all I need for this question?