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The set of permutations of a set A forms a group under

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So aka the symmetric group. And as I said so I have to give you a set and an operation remember so the set is all permutations.

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The origins of Group Theory in Abstract Algebra were

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In Group Theory from Abstract Algebra, given two permutations α and β written in array notation, we find their inverses α^-1 and ...

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I note a shorter formula for one of the rotations and one of the reflections in the dihedral group. We use this to discover that we can ...

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We present the symmetric group and a shorthand known as cycle notation for easily performing calculations.

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