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What is an alternating group and what is their importance in the permutation?
what is an alternating group and what is their importance in the permutation?
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Deepak singh 1
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alternating group An of Sn are collection of even permutation of Sn . Some important points . 1. An is subgroup of Sn 2. An is normal subgroup of Sn 3. Index of An in Sn is 2 4. order of An is n!/2 eg. in S3 , A3 is normal subgroup of order 3 . see attached example.
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Jagat Chaudhary![best-answer]()
The alternating group is a group containing only even permutations of the symmetric group. It turns out that half the permutations of the symmetric group are even and the other half are odd. That is if we permute a set with 'n' elements the symmetric group has !n permutations and the alternating group has !n/2 permutations. The alternating group is important from a mathematical point of view because, for A5 and above, it is a simple group which means it cannot be factored into smaller groups. It therefore plays an important pat in the categorization of groups. Jagat Chaudhary Eduncle Expert (MA)