MAT_305Review1

MAT_305Review1 - S n , A n , D n . 3. Theorems, Lemmas,...

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MAT 305 Review for Test 1 1. Important Definitions : groups, subgroups, subroup lattice, order of an element, Abelian groups, order of a group, Euler phi-function, cyclic groups, generators of cyclic groups, permutations, groups of permutations, odd even permutations, alternating groups, groups of symmetries, cosets, index = number of distinct cosets, homomorphisms, isomorphisms, Kernel of a homomorphism 2. Examples : Read all the examples in the sections we covered. You should be able to come up with examples for all the definitions above. You should know very well all the examples of groups introduced in section1.1. In addition you should be very familiar with the groups,
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Unformatted text preview: S n , A n , D n . 3. Theorems, Lemmas, Propositions, Corollaries : We discussed in class : 1.1.24, 1.2.17, 1.3.11, 1.3.12, 1.3.13, 1.3.14, 1.3.16, 1.3.20, 1.3.21, 1.3.23, 1.3.24, 1.4.10, 1.4.12, 1.4.34, 1.4.36, 2.1.3, 2.1.8, 2.1.9, 2.1.13, 2.1.16, 2.2.15( parts 1 thru 4), 2.2.16, 2.2.17, 2.2.23 (parts1, 2,3) and 2.2.25 4. Advice: 1. Read your notes carefully, 2. Read all the relevant sections in the book, 3. Redo all the homework problems without looking at your notes or book, 4 4. Do more problems from the book without looking at your notes or book....
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