KpopStarlet
Tue Aug 13 2024
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7 answers
1469
Why is it called abelian?
Excuse me, could you please elaborate on the term "abelian" and why it is so named? I understand it has something to do with mathematics, but I'm curious about the historical context and the specific reason behind the terminology. Is it named after a particular mathematician or does it stem from a specific mathematical concept? Your insight would be greatly appreciated.
KDramaLegendaryStarlight
Tue Aug 13 2024
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6 answers
1284
Are all cyclic groups abelian?
Are all cyclic groups inherently abelian in nature? It's a question that delves into the heart of group theory, specifically examining the relationship between cyclicity and commutativity within groups. Could it be that the very definition of a cyclic group, as one generated by a single element, inherently implies that any two elements within it can be rearranged without altering the result of their operation? Or is there a subtle distinction between these two concepts that prevents us from making such a blanket statement? Let's delve deeper into the matter and explore the intricacies of cyclic groups and their relationship with abelian groups.
KimonoGlitter
Tue Aug 13 2024
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6 answers
1093
Is the group Z abelian?
Could you please clarify for me if the group Z, also known as the integers under addition, possesses the property of being abelian? I understand that in an abelian group, the order of elements in a binary operation does not affect the result, so is it true that for any two integers a and b in Z, the sum a + b equals b + a? It would be helpful if you could elaborate on the concept of an abelian group and how it applies to the specific case of Z.
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.
