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Why $\mathbb{Q}$-vector space has no $\mathbb{Q}$-torsion?

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#vector-spaces #modules #rational-numbers #torsion-groups
602
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Every finitely generated module of a PID is a direct sum of a free module and of a torsion module

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#modules #principal-ideal-domains #finitely-generated #free-modules #torsion-groups
63
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class of abelian groups

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#modules #abelian-groups #direct-sum #finitely-generated #torsion-groups
413
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Trivial torsion subgroup

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#elliptic-curves #torsion-groups
2.4k
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Abstract Algebra. Let $\mathit{G} $ be an abelian group. Show that the elements of finite order in $\mathit{G}$ form a subgroup of $\mathit{G}$.

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#abstract-algebra #group-theory #abelian-groups #torsion-groups
843
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Is an abelian group the sum of a torsion group with a free group?

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#group-theory #abelian-groups #direct-sum #torsion-groups
168
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Hypercentral Groups and its abelianizations

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#abstract-algebra #group-theory #torsion-groups
455
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Coefficients of an elliptic curve for which the torsion group is trivial

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#number-theory #elliptic-curves #torsion-groups
617
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Why is the method to finding the order of a torsion subgroup different than finding the maximum order of a given element of a direct product?

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#abstract-algebra #torsion-groups
181
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Elliptic Curves Nagell-Lutz question

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#elliptic-curves #torsion-groups
187
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Nilpotent group with torsion divisible abelian quotient

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#group-theory #abelian-groups #solvable-groups #infinite-groups #torsion-groups
398
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Reduction map on torsion of elliptic curves

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#elliptic-curves #arithmetic-geometry #torsion-groups
355
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Torsion elements in integer-modules

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#group-theory #ring-theory #torsion-groups
643
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Computation of the 2-torsion group of an elliptic curve

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#finite-fields #elliptic-curves #torsion-groups
129
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Proving that some property on a chain complex of groups implies isomorphism between direct sums of these groups.

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#homological-algebra #abelian-groups #homology-cohomology #direct-sum #torsion-groups

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