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    Abstract Algebra : Permutations, Binary Operations and Mappings

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    Consider a non-empty set A. Prove that S(A) is closed in (M(A),o).
    Meaning: "o" is the composition of functions which defines a binary operation on M(A), the set of all maps from A to A. You need to prove that the set of all permutations on A is closed under the composition.

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    Solution Preview

    Inverses exist in S(A) because each f : A --> A in S(A) is bijective, hence has an ...

    Solution Summary

    Permutations, Binary Operations and Mappings are investigated. The solution is detailed and well presented.