# Abstract Algebra : Permutations, Binary Operations and Mappings

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.

https://brainmass.com/math/combinatorics/abstract-algebra-permutations-binary-operations-mappings-145364

#### 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.

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