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Published:
Sep 12, 2023Keywords:
Symmetric group Permutation Dihedral group Generators Relations Cayley’s Theorem
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Characterization of a class of Symmetric Group
Abstract
This paper studies a class of permutation group on a nonempty set X = {1, 2, 3, . . . , n} that maps even integer to even integer and odd integer to odd integer. We concluded that this collection of permutations, Bn is a group and that if n is even Bn = (Sn/2)2 but if n is odd Bn = S(n+1)/2 × S(n−1)/2.
