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MATH 531: Some topics we covered in Chapters 5-11
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Permutations - notation & operations
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Cycles; the cycle decomposition of a permutation & its uses
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Transpositions; even & odd permutations; the subgroup An
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Isomorphism (the relation) of groups; it's an equivalence relation
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Isomorphisms (functions) & homomorphisms
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Properties preserved by isomorphism (Abelian, cyclic, orders of
elements)
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Determining whether groups are isomorphic
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Automorphisms, including conjugation
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Cosets & their properties
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Lagrange's Theorem (the order of a subgroup divides the order of
the group)
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Applications (groups of prime order, Fermat's Little Theorem,
Euler's Theorem)
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Normal subgroups (pp. 172-173): characterizations via cosets &
conjugation
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Direct product of groups (pp. 150-154)
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When is a direct product cyclic?
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Fundamental Theorem of finite Abelian groups (pp. 211-213)
Allen D Bell
4/23/2004