Test_3_review_questions.pdf  Note!  There are a couple of mistakes on this sheet!  Specifically:

- In the answer to Problem 8 part d, in should say Z_2 x Z_2 instead of Z_4.

- The directions for part d should ask for a homomorphism from G to K.  (Not a homomorphism from G/H to K.)

- In Problem #10, it should be D_12.  (Not D_8.)

Also, I forgot to include the most basic eamples of all in the "Test 3 review questions."  Namely, do the following:

Let G=Z.  Let H=47Z={n in G such that n is divisible by 47}.  Show that H is normal in G and that G/H is isomorphic to Z_47.  Note that the elements of G/H are H, 1+H, 2+H, 3+H, . . . , 46+H.

Similarly, show that Z/12Z is isomorphic to Z_12.

Concepts_section_14_problem_23.doc

Section_13_Problem_32.pdf

Basic_Statements_for_the_Final.doc