MountFujiView
Wed Aug 14 2024
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7 answers
1121
Why is D3 not abelian?
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?
Arianna
Mon Aug 12 2024
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6 answers
968
Why is S4 not abelian?
I'm curious to understand why the group S4, which represents the set of all permutations of four distinct elements, is not abelian. Can you explain the underlying mathematical principles that lead to this non-abelian property? Specifically, what are the key differences in the behavior of elements within S4 compared to abelian groups, and how do these differences manifest in terms of the group's operation?
