POSSIBLE TEST AND QUIZ QUESTIONS

Many quiz and test questions will be selected from the following list. The key to doing well in the class is to do as many of these exercises as possible. (The list will be updated as we go along.) Once you have done all these problems, then you should work other exercises for additional practice.

 Chapter 3, Groups: 2, 6, 7, 12, 10, 13, 14, 17, 21, 25, 26, 27, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 45, 46, 47, 48, 49, 50, 51, 53, 53, 54
 Chapter 4, Cyclic Groups: 2, 4, 5, 8, 10, 11, 12, 20, 23, 24, 25, 26, 27, 28, 31, 33, 37, 38
 Chapter 5, Permutation Groups: 1, 2, 3, 7, 10, 17, 18, 22, 23, 27, 31,34
 Chapter 6, Cosets and Lagrange's Theorem: 3, 4, 5, 9, 12, 14, 16, 17, 18, 19, 21
 Chapter 9, Isomorphisms: 2, 5, 7, 8, 9, 16, 18, 22, 26, 27, 48, 50, 52
 Chapter 10, Normal Subgroups: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13
 Chapter 11, Homomorphisms: 2, 5, 6, 8, 10, 12, 14, 15, 16, 18, 23, 24, 27, 32
 Chapter 13, Structure of Groups: 1, 2, 3, 5, 6, 8
 Chapter 16, Rings: 2, 3, 7, 8, 11, 16, 17, 18, 18abc, 19, 24, 26, 27, 28, 30, 36, 37
 Chapter 17, Polynomials: 1, 2, 3, 5, 6, 7, 9, 10, 12, 13, 15, 17, 24, 26
 Chapter 18, Integral Domains: 1, 2, 4, 5, 11,16


You should also know and internalize (not memorize) the following results. Although it is a good idea to have a rudimentary idea of how the proofs work, the main thing is that you be able to apply these results when necessary to solve other problems. You should also know the definitions of all the terms which appear in these results.

Proposition 3.4 Proposition 3.17 Proposition 3.18 Proposition 3.19 Proposition 3.20 Proposition 3.21 Proposition 3.22
Theorem 3.23 Proposition 3.30 Proposition 3.31        
Theorem 4.3 Theorem 4.9 Theorem 4.10 Corollary 4.11 Theorem 4.13 Corollary 4.14 Proposition 4.24
Theorem 5.1 Theorem 5.9 Proposition 5.12 Theorem 5.15 Theorem 5.16 Proposition 5.17  
Lemma 6.3 Theorem 6.8 Theorem 6.10 Corollary 6.11 Corollary 6.12 Corollary 6.13  
Theorem 9.6 Theorem 9.7 Theorem 9.8 Corollary 9.9 Theorem 9.10 Theorem 9.12  
Theorem 10.3 Theorem 10.4 Proposition 11.4 Theorem 11.5 Theorem 11.10    
Theorem 13.4 Theorem 13.10          
Proposition 15.1 Proposition 15.2 Proposition 15.3 Theorem 15.4 Proposition 15.6 Proposition 15.7 Proposition 15.8
Proposition 16.10 Theorem 16.29 Theorem 16.30 Theorem 16.31 Theorem 16.35 Proposition 16.28  
Theorem 16.1 Proposition 16.2 Theorem 16.4 Corollary 16.5 Corollary 16.6 Theorem 16.12 Theorem 16.13

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