HW due Fri Nov 17
1. Let G act diagonally on unordered pairs of group elements, g.{a,b} = {ga,gb}.
Describe the set of orbits, and the stabilizers, and (for G finite) the formula |pairs| = sum |orbits|.
[Some people asked whether a can equal b. Answer: the math doesn't particularly care. You may as well leave that possibility out, since it's kinda dumb. If you've already written this up with a=b allowed, that's fine too.]
2. Let Sn act on itself by conjugation. Explain how to compute the size of the conjugacy class of a permutation pi. What equation do you get for S5?
(I.e. 5! = sum |conjugacy classes|, what are they?)
[H]
1.5 #18
1.6 #1,5,11
Describe the set of orbits, and the stabilizers, and (for G finite) the formula |pairs| = sum |orbits|.
[Some people asked whether a can equal b. Answer: the math doesn't particularly care. You may as well leave that possibility out, since it's kinda dumb. If you've already written this up with a=b allowed, that's fine too.]
2. Let Sn act on itself by conjugation. Explain how to compute the size of the conjugacy class of a permutation pi. What equation do you get for S5?
(I.e. 5! = sum |conjugacy classes|, what are they?)
[H]
1.5 #18
1.6 #1,5,11
posted by Allen Knutson @ 2:43 PM
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