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Show that the alternating group $A_{n}$ is nonabelian for $n\geq 4$.

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#group-theory #abelian-groups
417
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Torsion part of an Abelian group

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#abstract-algebra #group-theory #abelian-groups
46
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Find all the subgroups of this group

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#linear-algebra #group-theory #abelian-groups
15.4k
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Proof that every group of order 4 is abelian

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#abstract-algebra #group-theory #proof-verification #finite-groups #abelian-groups
109
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Parsing the Bockstein morphism

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#algebraic-topology #abelian-groups #exact-sequence
642
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$C_m \times C_n$ isomorphic to $C_{mn}$

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#group-theory #abelian-groups #cyclic-groups #group-isomorphism #coprime
91
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Is the quotient of a tensor product by a group a free module

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#commutative-algebra #tensor-products #abelian-groups #group-actions #free-modules
78
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Structure of countable infinite abelian torsion groups

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#group-theory #reference-request #abelian-groups
41
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The cardinal of some set of cosets is countable

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#group-theory #finite-groups #abelian-groups
54
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A small problem on the annihilators of some subgroups

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#group-theory #abelian-groups #locally-compact-groups
677
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How to define a lattice as an abelian group?

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#group-theory #abelian-groups #integer-lattices
132
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I believe all groups are necessarily finitely or infinitely generated. Is that correct?

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#group-theory #finite-groups #abelian-groups #finitely-generated
127
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Finite-dimensional complex representation of finitely-generated abelian group - completely reducible?

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#group-theory #representation-theory #abelian-groups
91
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Complicated Proof of Free Group Generators by $n$ elements implies $\operatorname{Rank}(F) \le n$

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#abstract-algebra #abelian-groups #finitely-generated
244
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Are all non-abelian groups not simple?

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#group-theory #abelian-groups #simple-groups

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