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relationship between Torsion and Relations

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#group-theory #group-presentation #combinatorial-group-theory #torsion-groups
153
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Examples of an abelian group whose torsion subgroup is not a direct summand

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#group-theory #examples-counterexamples #abelian-groups #exact-sequence #torsion-groups
120
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Proof verification of decomposition of abelian group into torsion and free groups

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#group-theory #solution-verification #abelian-groups #torsion-groups #free-abelian-group
82
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Is the extension of a torsion free group by a torsion free group necessarily torsion free?

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#group-theory #examples-counterexamples #infinite-groups #torsion-groups
58
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$\underset{p\in \mathbb{P}}{\prod}\mathbb{Z}/p\mathbb{Z}$ is non splitting mixed abelian group.

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#abstract-algebra #group-theory #prime-numbers #abelian-groups #torsion-groups
31
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$\prod_p \mathbb{Z}/p\mathbb{Z}$ is not the direct sum of $\bigoplus_p \mathbb{Z}/p\mathbb{Z}$ and a torsion-free subgroup

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#abelian-groups #free-groups #infinite-groups #torsion-groups
41
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Maximal Essential Extension of Abelian Groups

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#homological-algebra #abelian-groups #torsion-groups
77
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Decomposition of infinite abelian groups

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#group-theory #abelian-groups #infinite-groups #torsion-groups
87
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Let $E:y^2=x(x-a)(x-b)(a,b\in \Bbb{Q})$ be an elliptic curve. What is $\#E_d(\Bbb{Q})_{tor}$?

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#number-theory #elliptic-curves #arithmetic-geometry #abelian-varieties #torsion-groups
43
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Intersection between torsion cycles and free cycles

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#intersection-theory #torsion-groups #4-manifolds
38
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In what sense is cotorsion dual to torsion?

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#abstract-algebra #homological-algebra #torsion-groups
33
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Torsion spin-c structures on $S^1\times S^2$

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#low-dimensional-topology #spin-geometry #gauge-theory #torsion-groups #cobordism
103
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Determining the size of an $m$-torsion group of elliptic curves over finite fields

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#finite-fields #elliptic-curves #sagemath #torsion-groups
69
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Show that all the element of $ \mathbb{Q} / \mathbb{Z} $ are of torsion.

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#abstract-algebra #group-theory #solution-verification #rational-numbers #torsion-groups
61
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Is $\mu_p$ the only nontrivial Galois module of size $p$?

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#galois-theory #elliptic-curves #torsion-groups

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