Lucia
Wed Aug 14 2024
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5 answers
1404
Is d4 not abelian?
Excuse me, could you please clarify for me if the group denoted as d4 is indeed not abelian? I understand that in mathematics, an abelian group is one in which the group operation is commutative, meaning that the order of the elements being operated on does not affect the result. So, in the context of d4, which I assume refers to the dihedral group of order 4, is it the case that the multiplication of its elements does not satisfy this commutative property? I'm curious to know if there's a specific reason why d4 is not considered an abelian group.
Lucia
Wed Aug 14 2024
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7 answers
1837
Is Z an abelian group?
Could you please elaborate on why you believe that Z, as it is commonly understood in mathematics and cryptography, may or may not constitute an abelian group? Are you referring to the set of integers under addition, or perhaps another interpretation of Z in a specific context? In either case, could you explain the properties that make an abelian group distinct, and how those properties either apply or do not apply to Z? Furthermore, if Z is indeed an abelian group in your view, could you provide examples to support your argument? Alternatively, if it's not, could you clarify the reasons why and possibly suggest alternative groups that do satisfy the conditions of an abelian group?
RainbowlitDelight
Wed Aug 14 2024
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7 answers
1441
Which group of order is abelian?
Could you please elaborate on which group of order you are referring to when asking if it is abelian? In mathematics, a group is considered abelian if its operation is commutative, meaning that for any two elements a and b in the group, the result of the operation a applied to b is the same as the result of b applied to a. This property is not inherent to all groups, so it's important to specify the group in question to determine if it is indeed abelian.
Lorenzo
Tue Aug 13 2024
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6 answers
1216
Can abelian group be infinite?
I'm curious about the concept of abelian groups and their potential to be infinite. Can you elaborate on whether or not an abelian group can indeed be infinite in nature? It's intriguing to ponder the implications of an abelian group that doesn't have a finite number of elements, especially in the context of abstract algebra. Could you provide some insight into this idea, perhaps by discussing examples or properties that may suggest the possibility of an infinite abelian group?
Claudio
Tue Aug 13 2024
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7 answers
1406
Is an abelian group closed?
Could you please clarify for me if an abelian group is indeed closed under its operation? I understand that an abelian group satisfies the properties of associativity, identity, inverses, and commutativity, but I'm specifically wondering about its closure. Does the fact that it is a group inherently mean that it is closed, or is there something specific about an abelian group that guarantees closure? I would appreciate your insight on this matter.
