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 %%%%%%%% 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