Homework 13, due 11/23/2015
1. Artin 7.1.1
2. Artin 7.2.1
3. Artin 7.2.9 (we haven’t defined the quaternion group–just look it up in
Artin)
4. Artin 7.3.2
5. Artin 7.3.3
6. Let p be an odd prime. In class we constructed a non-abelian group of
order p3 by taking the subgroup


1 x z
Hp = 0 1 y  ⊂ GL3 (Fp ).
0 0 1
Construct a non-abelian group of order p3 that is not isomorphic to Hp .
7. Describe, with proof, all abelian groups of order p3 . (Between this exercise
and the previous one, you have in fact seen all isomorphism classes of
groups of order p3 –you may want to think about why, but you don’t need
to prove it on the homework.)
8. Artin 7.4.5
9. Artin 7.4.6
1