Cryptocurrency Q&A Is alternating group abelian?

Is alternating group abelian?

Giulia Giulia Mon Aug 12 2024 | 6 answers 1762
Could you please clarify for me, why are we asking if the alternating group is abelian? As I understand, the alternating group is a subgroup of the symmetric group that consists only of even permutations. Abelian groups, on the other hand, are groups where the operation is commutative, meaning that for any two elements a and b in the group, the operation a * b equals b * a. So, are we exploring if the alternating group exhibits this commutative property? Or is there another specific reason we're posing this question? Is alternating group abelian?

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SsangyongSpiritedStrengthCourage SsangyongSpiritedStrengthCourage Wed Aug 14 2024
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DongdaemunTrendsetting DongdaemunTrendsetting Wed Aug 14 2024
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PulseEclipse PulseEclipse Wed Aug 14 2024
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CryptoMystic CryptoMystic Tue Aug 13 2024
The alternating groups represent an important class of groups in mathematics, with specific properties that make them useful in various applications. Notably, the group An is abelian (meaning it is commutative) if and only if n is less than or equal to 3, and simple (meaning it has no non-trivial normal subgroups) if and only if n is 3 or greater than or equal to 5.

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