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Additions to the MAT 1100 web site no longer count towards good deed points
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Week of...
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Notes and Links
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1
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Sep 13
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About This Class, Tuesday - Non Commutative Gaussian Elimination, Thursday
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2
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Sep 20
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Tuesday - Homomorphisms and Normal Groups, Thursday - Isomorphism Theorems
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3
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Sep 27
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Class Photo, HW1, HW1 solution
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4
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Oct 4
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5
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Oct 11
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HW2, HW2 solution
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6
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Oct 18
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7
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Oct 25
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Term Test
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8
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Nov 1
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HW3, HW3 solution
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9
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Nov 8
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Monday-Tuesday is Fall Break, One Theorem, Two Corollaries, Four Weeks
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10
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Nov 15
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HW4, HW4 solution
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11
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Nov 22
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12
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Nov 29
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HW5, HW5 solution
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13
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Dec 6
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Boxing Day Handout, see also December 2010 Schedule. Some Class Notes
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F
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Dec 13
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Final exam, Tuesday December 14 10-1, Bahen 6183
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Register of Good Deeds
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Add your name / see who's in!
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See Non Commutative Gaussian Elimination
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This assignment is due at class time on Thursday, October 21, 2010.
Solve the following questions
- (Selick)
- What it the least integer for which the symmetric group contains an element of order 18?
- What is the maximal order of an element in ? (That is, of a shuffling of the red cards within a deck of cards?)
- (Selick) Let be a subgroup of index 2 in a group . Show that is normal in .
- Let be a permutation whose cycle decomposition consists of one 5-cycle, two 3-cycles, and one 2-cycle. What is the order of the centralizer of ?
- (Selick) Let be a group of odd order. Show that is not conjugate to unless .
- (Dummit and Foote) Show that if is cyclic then is Abelian.
- (Lang) Prove that if the group of automorphisms of a group is cyclic, then is Abelian.
- (Lang)
- Let be a group and let be a subgroup of finite index. Prove that there is a normal subgroup of , contained in , so that is also finite. (Hint: Let and find a morphism whose kernel is contained in .)
- Let be a group and and be subgroups of . Suppose and . Show that