Symmetric Group

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symmetric group

[sə′me·trik ′grüp]
The group consisting of all permutations of a finite set of symbols.

Symmetric Group


A symmetric group of order n is a group consisting of all possible permutations of n objects. Such a group has n! elements. The permutations of n objects with an even number of inversions form an alternating subgroup of the symmetric group; this alternating subgroup has n!/2 elements.

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In [VT07], Tsilevich and Vershik extend this setting to study the infinite symmetric group [S.