Valentina
Sat Sep 21 2024
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6 answers
1716
Is every abelian group normal?
I'm curious about a fundamental concept in group theory. Can you clarify for me: is it true that every abelian group is necessarily normal? It seems that abelian groups possess a certain level of symmetry and commutativity, which might suggest they inherently possess the properties of normality. However, I'm unsure if this is always the case. Could you elaborate on the relationship between abelian groups and normality, and if there are any exceptions or nuances to this potential connection?
CryptoWanderer
Wed Sep 18 2024
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5 answers
1376
Is an abelian group simple?
Could you please clarify for me if an abelian group is necessarily simple? I understand that an abelian group is a group where the operation is commutative, but I'm unsure if this property alone implies simplicity. Are there any specific conditions or properties that an abelian group must possess in order to be considered simple, or are there examples of abelian groups that are not simple? I'm particularly interested in understanding the relationship between abelian groups and simplicity in the context of group theory.
BonsaiBeauty
Wed Sep 18 2024
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5 answers
1069
What is an example of an abelian group?
Could you provide an example of an abelian group, perhaps with a clear explanation of its properties? It would be helpful to understand how the elements of this group interact with each other under the operation defined, and why this group is considered to be abelian in nature. By breaking it down in this way, it may be easier for those who are new to the concept to grasp the fundamental principles of abelian groups.
CryptoQueenGuard
Wed Sep 18 2024
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6 answers
1528
Is abelian group closed?
Excuse me, could you please clarify something for me? The paragraph mentions the term "abelian group," and I'm wondering if it is indeed closed. By closed, I mean does the set of elements within the abelian group satisfy the property that for any two elements in the group, their operation results in another element that is also within the group? I'm asking because I'm trying to understand the fundamental properties of abelian groups and how they relate to other algebraic structures.
Maria
Tue Sep 17 2024
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7 answers
1413
Why is abelian group important?
Why is the concept of an abelian group significant in the realm of mathematics and cryptography? Could you elaborate on its fundamental properties and how they contribute to the security and efficiency of various systems, such as blockchain technologies? Additionally, could you provide some real-world examples where abelian groups play a crucial role?
