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This document defines and discusses cyclic permutations and transpositions in the symmetric group. It begins by defining a cyclic permutation as one that moves elements in a set cyclically while fixing others. It then proves that a cyclic permutation of length m has order m. It defines a transposition as a cycle of length 2 that interchanges two elements. The main results are: 1) Every cycle can be expressed as a product of transpositions. 2) Every permutation can be expressed as a product of transposit

Author

Hafiz Azeem

Language

EN