Michele
Wed Aug 14 2024
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7 answers
1273
Is the S4 abelian?
Can you explain to me, in simple terms, whether the group S4 is abelian or not? It's a question that often comes up in discussions related to group theory and cryptography, and I'm curious to understand the answer. What properties does S4 possess that might indicate whether it's abelian or not? Could you provide an example or two to help clarify your explanation?
Emanuele
Tue Aug 13 2024
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6 answers
1615
Are S4 and D12 isomorphic?
Could you please clarify for me the specific context in which S4 and D12 are being discussed? Are they both groups, perhaps related to mathematical structures or cryptographic protocols? Assuming they are indeed groups, the question "Are S4 and D12 isomorphic?" seeks to determine if there exists a bijective homomorphism between the two groups that preserves the group operation. This means that there should be a way to map elements of S4 to elements of D12 in such a way that the group operation (e.g., multiplication or composition) behaves identically under this mapping. Do you have any additional information or specific definitions of S4 and D12 that could help us explore this question further?
Arianna
Mon Aug 12 2024
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6 answers
968
Why is S4 not abelian?
I'm curious to understand why the group S4, which represents the set of all permutations of four distinct elements, is not abelian. Can you explain the underlying mathematical principles that lead to this non-abelian property? Specifically, what are the key differences in the behavior of elements within S4 compared to abelian groups, and how do these differences manifest in terms of the group's operation?
