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Abelian group is torsion if tensor product with reals is zero.

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#abstract-algebra #commutative-algebra #modules #tensor-products #abelian-groups
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Non-Abelian groups with all proper subgroups Abelian

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#abstract-algebra #group-theory #abelian-groups
95
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infinite direct product of integers is not an essential submodule of infinite direct product of rationals.

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#modules #abelian-groups
841
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Classification of finite rank Abelian groups

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#abstract-algebra #group-theory #abelian-groups #torsion-groups
130
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abelian group, direct summand

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#modules #abelian-groups #exact-sequence #direct-sum
309
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Group of order 144

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#abstract-algebra #group-theory #abelian-groups
66
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Homomorphism and abelian group.

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#abstract-algebra #group-theory #abelian-groups #group-homomorphism
787
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Is there a good example of a subgroup of an infinitely generated abelian group that is not isomorphic to a quotient of that group?

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#abstract-algebra #group-theory #abelian-groups #infinite-groups
448
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Decomposing an abelian extension into cyclic extensions

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#galois-theory #extension-field #abelian-groups
47
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Abelian group quotient computation

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#abstract-algebra #group-theory #abelian-groups #quotient-group
119
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Defining set-theoretic section on finite abelian group

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#group-theory #finite-groups #abelian-groups
64
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What is an example where $G(p)/H(p) \not \cong (G/H)(p)$?

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#group-theory #finite-groups #abelian-groups
58
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How to prove that this group is abelian?

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#abstract-algebra #group-theory #abelian-groups
121
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If a group isomorphism is an involution with only a trivial fixed point, then the group is abelian

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#abstract-algebra #group-theory #abelian-groups #group-isomorphism
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Isomorphisms of finite abelian groups

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#group-theory #finite-groups #abelian-groups #group-isomorphism

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