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1. • CommentRowNumber1.
   • CommentAuthorRichard Williamson
   • CommentTimeMar 31st 2021
   • PermaLink
   Author: Richard Williamson
   Format: MarkdownItexLinking to the new page [[torsion points of an elliptic curve]]. <a href="https://ncatlab.org/nlab/revision/diff/torsion+subgroup/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/torsion+subgroup/16">v16</a>, <a href="https://ncatlab.org/nlab/show/torsion+subgroup">current</a>

   Linking to the new page torsion points of an elliptic curve.

   diff, v16, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 8th 2021
   • (edited Dec 8th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have expanded the Examples-section ([here](https://ncatlab.org/nlab/show/torsion+subgroup#ExamplesAndApplications)), making explicit how tensor product with the rationals removes torsion in abelian groups. Also expanded the Definition-section slightly ([here](https://ncatlab.org/nlab/show/torsion+subgroup#Definition)), highlighting how the torsion condition looks for abelian groups. <a href="https://ncatlab.org/nlab/revision/diff/torsion+subgroup/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/torsion+subgroup/17">v17</a>, <a href="https://ncatlab.org/nlab/show/torsion+subgroup">current</a>

   I have expanded the Examples-section (here), making explicit how tensor product with the rationals removes torsion in abelian groups.

   Also expanded the Definition-section slightly (here), highlighting how the torsion condition looks for abelian groups.

   diff, v17, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 8th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso added pointer to * [[Spencer Ernst Dickson]], *A Torsion Theory for Abelian Categories*, Transactions of the American Mathematical Society **121** 1 (1966) 223-235 ([doi:10.2307/1994341](https://doi.org/10.2307/1994341), [jstor:1994341](https://www.jstor.org/stable/1994341)) (previosuly only the 1963 thesis was mentioned, while in related entries it was the other way around, am harmonizing this now) <a href="https://ncatlab.org/nlab/revision/diff/torsion+subgroup/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/torsion+subgroup/17">v17</a>, <a href="https://ncatlab.org/nlab/show/torsion+subgroup">current</a>

   also added pointer to

   • Spencer Ernst Dickson, A Torsion Theory for Abelian Categories, Transactions of the American Mathematical Society 121 1 (1966) 223-235 (doi:10.2307/1994341, jstor:1994341)

   (previosuly only the 1963 thesis was mentioned, while in related entries it was the other way around, am harmonizing this now)

   diff, v17, current

4. • CommentRowNumber4.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 19th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexDoes the statement > An [[abelian group]] is torsion-free precisely if regarded as a $\mathbb{Z}$-[[module]] it is a [[flat module]]. hold in constructive mathematics? The current proof uses excluded middle. Anonymous <a href="https://ncatlab.org/nlab/revision/diff/torsion+subgroup/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/torsion+subgroup/19">v19</a>, <a href="https://ncatlab.org/nlab/show/torsion+subgroup">current</a>

   Does the statement

   An abelian group is torsion-free precisely if regarded as a $\mathbb{Z}$-module it is a flat module.

   hold in constructive mathematics? The current proof uses excluded middle.

   Anonymous

   diff, v19, current

5. • CommentRowNumber5.
   • CommentAuthorJ-B Vienney
   • CommentTimeFeb 17th 2023
   • (edited Feb 17th 2023)
   • PermaLink
   Author: J-B Vienney
   Format: MarkdownItexThere is a serious mistake in this entry: the "torsion subgroup" of a non-abelian group is not necessarily a group... Examples of two elements of finite order whose product is not of finite order are given [here](https://math.stackexchange.com/questions/41303/examples-and-further-results-about-the-order-of-the-product-of-two-elements-in-a). Am I wrong?

   There is a serious mistake in this entry: the “torsion subgroup” of a non-abelian group is not necessarily a group… Examples of two elements of finite order whose product is not of finite order are given here. Am I wrong?

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeFeb 17th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded the abelianness condition. <a href="https://ncatlab.org/nlab/revision/diff/torsion+subgroup/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/torsion+subgroup/21">v21</a>, <a href="https://ncatlab.org/nlab/show/torsion+subgroup">current</a>

   Added the abelianness condition.

   diff, v21, current