HanRiverWave
Tue Aug 13 2024
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6 answers
968
Is S5 abelian?
Can you clarify for me if the group S5, which refers to the symmetric group on 5 elements, is abelian? To better understand, I'd like to know if the multiplication of any two elements in S5, when performed in either order, results in the same outcome. In other words, is the commutative property of multiplication satisfied by all elements in S5? This would be crucial in determining whether S5 is indeed an abelian group or not.
VoyagerSoul
Tue Aug 13 2024
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5 answers
1164
Does abelian imply normal?
Excuse me, but I've been pondering over this mathematical concept and I'm a bit confused. Can you clarify for me if the term "abelian" inherently implies that a group is also "normal"? It seems like there might be some overlap in properties, but I'm not entirely sure. Could you please explain the relationship, if any, between these two concepts in simple terms? Thank you for your time and assistance.
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?
