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/. Note that G/ 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
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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.)
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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