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Unformatted text preview: (*)Theorem 6.4 Aut ( G ) and Inn ( G ) are Groups (*)Lemma pg. 138 Properties of Cosets Theorem 7.1 Lagrange’s Theorem Corollary 1 [ G : H ] =  G   H  (*)Corollary 2  a  Divides  G  (*)Corollary 3 Groups of Prime Order are Cyclic (*)Corollary 4 a  G  = e Theorem 8.1 Order of an Element in a Direct Product Theorem 8.2 Criterion for G ⊕ H to Be Cyclic Corollary 1 pg. 156 Criterion for G 1 ⊕ G 2 ⊕ ··· ⊕ G n to Be Cyclic Corollary 2 pg. 156 Criterion for Z n 1 n 2 ··· n k = Z n 1 ⊕ Z n 2 ⊕ ··· ⊕ Z n k • Here are some practice problems from the textbook: Chapter 5: 2, 3, 4, 6, 7, 9, 12, 15, 17, 18, 22, 30, 38, 51 Chapter 6: 1, 3, 5, 11, 15, 19, 22, 25, 26, 35 Chapter 7: 1, 2, 3, 5, 7, 8, 13, 14, 23, 25, 26, 38, 39 Chapter 8: 2, 3, 5, 7, 8, 9, 11, 14, 17, 21, 23, 25, 31, 41 Chapter 10: 1, 2, 3, 4, 7...
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 Winter '08
 Wilson
 Math, Group Theory, Permutations, Symmetric group, Cosets Theorem, Theorem G Corollary, disjoint cycles Theorem

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