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Show that $\operatorname{Gal}((x^{8}-1)/(x-1))$ is abelian.

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#galois-theory #abelian-groups
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proof that special orthogonal group SO(2) is abelian group

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#abstract-algebra #group-theory #abelian-groups
725
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Abstract properties of the absolute Galois group over $\mathbb{Q}$

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#group-theory #galois-theory #abelian-groups #galois-extensions
1k
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Is it only the generator of the group that commutes with all the other elements?

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#abstract-algebra #group-theory #number-theory #abelian-groups #dihedral-groups
1k
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Why is every conjugacy class of an abelian group composed of a single element?

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#group-theory #number-theory #elementary-number-theory #abelian-groups
143
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About conjugation class functions in abelian groups.

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#abstract-algebra #group-theory #finite-groups #representation-theory #abelian-groups
44
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Every $f \in L^{1}(G)$ is product of two of $L^{2}(G)$

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#measure-theory #fourier-analysis #abelian-groups
348
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Homomorphism between free groups induced by group homomorphism of abelian groups.

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#group-theory #abelian-groups #group-homomorphism #finitely-generated
113
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On totally ordered abelian groups having exactly one convex subgroup

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#group-theory #abelian-groups #ordered-groups
35
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Coefficients of function on finite abelian group

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#finite-groups #abelian-groups #fourier-transform #characters
251
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Finitely-generated abelian groups in a long exact sequence

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#homological-algebra #abelian-groups #exact-sequence
27
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Plane symmetries of this shape

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#group-theory #abelian-groups #symmetric-groups
218
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Can one distinguish finite groups by their maps from abelian groups?

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#group-theory #finite-groups #category-theory #abelian-groups
846
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Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?

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#abstract-algebra #group-theory #ring-theory #modules #abelian-groups
59
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Prove that $H = \langle a, b \rangle$ is a subgroup of $G$.

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#group-theory #abelian-groups

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