Cryptocurrency Q&A Why is d4 not abelian?

Why is d4 not abelian?

GeishaMelody GeishaMelody Mon Aug 12 2024 | 5 answers 676
Could you please elaborate on why the group d4, often referred to as the dihedral group of order 8, is not considered abelian? It's my understanding that in an abelian group, the order of multiplication doesn't matter, i.e., for any two elements a and b in the group, a * b = b * a. However, with d4, which comprises rotations and reflections of a square, it seems the order in which we apply these transformations can yield different results. Could you explain why this property disqualifies d4 from being abelian? Why is d4 not abelian?

5 answers

OliviaTaylor OliviaTaylor Wed Aug 14 2024
The non-abelian nature of rotation and reflection operations in groups such as D4 highlights the complexity of certain mathematical constructs. This concept is not directly related to cryptocurrency or finance, but it serves as a reminder of the intricate nature of many systems, including those found in the digital asset space.

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CryptoAlchemyMaster CryptoAlchemyMaster Wed Aug 14 2024
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SamuraiCourageous SamuraiCourageous Wed Aug 14 2024
Cryptocurrency and finance are two intertwined fields that have gained significant attention in recent years. The rise of digital currencies has transformed the financial landscape, offering new opportunities for investment, trading, and payment processing. However, navigating this complex and ever-evolving space requires a deep understanding of the underlying technologies and market dynamics.

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Michele Michele Wed Aug 14 2024
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Giulia Giulia Wed Aug 14 2024
One of the key players in the cryptocurrency exchange space is BTCC, a top platform that offers a wide range of services to its users. From spot trading to futures contracts and digital wallet solutions, BTCC provides a comprehensive platform for those looking to engage in the cryptocurrency market.

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