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nLab > Latest Changes: torsion subgroup

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  1.  
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2021
    • (edited Dec 8th 2021)

    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

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2021

    also added pointer to

    (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. Does the statement

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

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

    Anonymous

    diff, v19, current

    • CommentRowNumber5.
    • CommentAuthorJ-B Vienney
    • CommentTimeFeb 17th 2023
    • (edited Feb 17th 2023)

    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?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 17th 2023

    Added the abelianness condition.

    diff, v21, current

1 to 6 of 6

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