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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

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