3330_Notes_4o2_fill

3330_Notes_4o2_fill - Math 3330 Section 4.2 Cayleys Theorem...

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Math 3330 Section 4.2 Cayley’s Theorem Theorem: All groups are isomorphic to a group of permutations. Proof: Let G be a group with operation *. For an element a of the group G, Consider the map given by : a fG G () a fx a x = It is a permutation – One-to-one – Onto – The SET G’ = { with the operation of function composition is a group. } : a fa G Proof: Closed? Associative?

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Identity? Inverses?

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3330_Notes_4o2_fill - Math 3330 Section 4.2 Cayleys Theorem...

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