Can you explain why the group D3, which is often associated with the symmetry of an equilateral triangle, is not considered to be abelian? I'm curious to understand the specific properties or characteristics of D3 that prevent it from fitting the definition of an abelian group. Could you elaborate on the mathematical reasons behind this classification and provide any relevant examples to help clarify your explanation?
7 answers
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It's also worth mentioning that the table mentioned earlier, which is not symmetrical across the main diagonal, is an example of a mathematical concept known as non-abelianity. This property has important implications for various fields, including cryptography and group theory.
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