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Unformatted text preview: Study sheet for Math 4107 midterm 2, Fall 2009 November 10, 2009 • Know all the material covered up to and including the first midterm. • Know what an automorphism and innerautomorphism are, and know that they form a group under composition. Know that the group of innerautomorphisms on a group G is isomorphic to G/Z , where Z is the center. Know how to show that every finite group G of order greater than 2 (including now groups of even order) has a nontrivial automorphism. Know that Aut(( Z /n Z ) + ) is isomorphic to ( Z /n Z ) * . • Know the definition of S n and A n (as I covered in class – S n is the sym metric group on { 1 , 2 ,...,n } , while A n is the corresponding alternating group). Know how to write every permutation as a product of disjoint cycles, and know how to use cycle notation. Know that every element of A n is a product of 3cycles. Know the general form of the conju gate of a permutation when written in disjoint cycle form – it basically has the same cycle structure. Know how many equivalence classes ofhas the same cycle structure....
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 Fall '08
 Staff
 Math, Algebra, Group Theory, Equivalence relation, Symmetric group, Conjugacy class, Sylow

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