MountFujiMystic
Thu Sep 19 2024
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7 answers
1713
Is D4 abelian or not?
Excuse me, could you please clarify whether D4, the dihedral group of order 8, possesses the property of being abelian or not? It would be greatly appreciated if you could elaborate on the reasoning behind your answer, as I am trying to understand the fundamental concepts of group theory and how they apply to specific groups like D4.
GeishaMelody
Mon Aug 12 2024
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5 answers
676
Why is d4 not abelian?
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?
