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nLab > Latest Changes: SL(2,Z)

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2019

    just for completeness and ease of hyperlinking

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2025

    briefly added the statement (here) that S,T∈SL 2(ℤ)S, T \in SL_2(\mathbb{Z}) generate that group

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2025

    also added statement of the presentation

    SL 2(ℤ)≃⟨S,T|S 4=e,(ST) 3=S 2⟩ SL_2(\mathbb{Z}) \;\simeq\; \big\langle S\,, T \,\big\vert\, S^4 = \mathrm{e} ,\, (S T)^3 = S^2 \big\rangle

    diff, v6, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2025

    mentioned also the alternative presentation

    SL 2(ℤ)≃⟨S,T|S 4=e,(TS) 3=e,S 2(TS)=(TS)S 2⟩. SL_2(\mathbb{Z}) \;\simeq\; \big\langle S, T \,\big\vert\, S^4 = \mathrm{e} ,\, (T S)^3 = \mathrm{e} ,\, S^2 (T S) = (T S)S^2 \big\rangle \,.

    (This is attributed by Blanc & Déserti 2012 §2.1 to Newman 1972, but I have trouble extracting this exact statement from Newman’s book.)

    diff, v7, current

1 to 4 of 4

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