Test 3 on Thursday Nov. 15.
---------------------------

Turn in answers for the following questions
on Thursday November 15. There will also be a test
on that day.

3.5.   10.
4.1.   7c, 8.
4.2.   8.
4.3.   24.

       30.  Hint: Let S = {x, x^(-1)}.  If |S|=1
            then x=x^(-1) and consider the subgroup <x>.

            If |S|=2 then consider the subgroup of all g
            in G for which gSg^(-1) = S    (you can think of
            this subgroup as the stabilizer of S, where
            G acts on subsets of G by conjugation).

            Show that if x is not 1, then in both cases
            you find a subgroup with even order.

4.4.   2, 13.

4.5.   18.

       22.  Hint: Compute the primes that divide 132,
            then for each p compute all possible values
            for n_p that are allowed by part (3) in
            theorem 18. Then use corollary 20.