Hello Algebra people, Magid and myself have a question. In question 14 of the assignment, we are asked to find the gs is S_n that preserve S_m under conjugation. I will state our question with an example. Suppose you have S_2 and S_3. Pick g = (1 2 3) g e g^-1 = e (3 2 1) (1 2) (1 2 3) = (1 3) Is g in the normalizer of S_2 in S_3. Because {e, (1 3)} is actually isomorphic to S_2, its a matter of relabeling. Our question orbits around that. Is equality g S_m g^-1 = S_m up to isomorphism?
Posted on: Mon, 13 Oct 2014 03:35:06 +0000
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