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In Preparation
The information below is preliminary and cannot be trusted! (v)
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Week of...
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Notes and Links
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Additions to the MAT 1100 web site no longer count towards good deed points
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1
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Sep 12
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About This Class, Tuesday - Non Commutative Gaussian Elimination, Thursday - NCGE completed, the category of groups, images and kernels.
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2
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Sep 19
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I'll be in Strasbourg, class was be taught by Paul Selick. See my summary.
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3
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Sep 26
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Class Photo, HW1, HW1 Submissions, HW 1 Solutions
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4
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Oct 3
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The Simplicity of the Alternating Groups
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5
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Oct 10
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HW2, HW 2 Solutions
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6
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Oct 17
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Groups of Order 60 and 84
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7
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Oct 24
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Extra office hours: Monday 10:30-12:30 (Dror), 5PM-7PM @ Huron 1028 (Stephen). Term Test on Tuesday. Summary for the midterm exam. Term Test - Sample Solutions
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8
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Oct 31
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HW3, HW 3 Solutions
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9
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Nov 7
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Monday-Tuesday is November Break, One Theorem, Two Corollaries, Four Weeks
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10
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Nov 14
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HW4, HW 4 Solutions
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11
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Nov 21
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12
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Nov 28
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HW5 and last week's schedule
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13
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Dec 5
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Tuesday - the Jordan form; UofT Fall Semester ends Wednesday; our Final Exam took place on Friday
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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 20, 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