Math 100A homework assignments and due dates 

HW #8  Due Wednesday noon, Nov. 30, 2011
Section 7.3, #7, 12
Hint for #7:  Show that Z(G) contains an element z of order p,
and look at the quotient group G/<z>.  Note that G/<z> has smaller
size than G, and  proceed by induction.
Hint for #12:  We will sketch a proof on Monday, but try it yourself
first if you'd like the challenge of discovering an appropriate
set S and a group action on S.  Problem 12 says that any subgroup 
of index p in G is normal in G, if p is the SMALLEST prime divisor of
|G|.  We already proved this for p=2 (i.e., any subgroup of G 
containing |G|/2 elements must be normal in G).  The proof for general p
is much more challenging.  
Example for #12:  If G has 45 elements and H is a subgroup with 15 elements,
then H must be normal in G.


HW #7  (Practice problems not to be handed in.)
Section 7.2, p. 330, #8,9,10,12,13,15,16,17,18 

HW #6:  Due Wednesday noon, Nov 16, 2011
Read pp. 319-321, then do
Section 7.1, p. 322, #2,3,5,9,11


HW #5 Due Wed noon, Nov 9, 2011
Section 3.7, p. 162, #1,7,14,18 
Section 3.8, p. 175, #1, #5,6,7,8,9
%%%%%%%%
Hint on #5:  Show that the map gH ----->  Hg'
from the set of all left cosets to the set of all right cosets
is one to one and onto.  (Here g' denotes the inverse of g.)
%%%%%%%%


HW #4 Due Wed noon, Nov 2, 2011
Section 3.6, p. 151, #8,9,19,21,22

HW #3  Due Wed noon, Oct 19, 2011
Section 3.2, p. 113, #5,11,12,14,15,19,21,23
Section 3.3, p. 114, #14

HW #2 Due Wed noon, Oct 12, 2011 (extended to Fri 5 pm, Oct 14)
Section 2.3, p. 85, #5-13.
Section 3.1, p. 102, #17, 23, 24


HW #1 Due Wed noon, Oct 5, 2011
p. 32, # 4, 10, 11, 12, 13, 18, 24, 26
p. 43, # 10, 12, 24, 27, 29