Fundamental domains for congruence subgroups of SL2 in positive characteristic

Lisa Carbone, Leigh Cobbs, Scott Murray

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma
    Original languageEnglish
    Pages (from-to)431-439
    Number of pages9
    JournalJournal of Algebra
    Volume325
    Issue number1
    DOIs
    Publication statusPublished - 2011

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    Fundamental Domain
    Congruence Subgroups
    Positive Characteristic
    Graph of Groups
    Computer algebra system
    Coset
    Subgroup

    Cite this

    Carbone, Lisa ; Cobbs, Leigh ; Murray, Scott. / Fundamental domains for congruence subgroups of SL2 in positive characteristic. In: Journal of Algebra. 2011 ; Vol. 325, No. 1. pp. 431-439.
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    Fundamental domains for congruence subgroups of SL2 in positive characteristic. / Carbone, Lisa; Cobbs, Leigh; Murray, Scott.

    In: Journal of Algebra, Vol. 325, No. 1, 2011, p. 431-439.

    Research output: Contribution to journalArticle

    TY - JOUR

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    AU - Carbone, Lisa

    AU - Cobbs, Leigh

    AU - Murray, Scott

    PY - 2011

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    AB - In this work, we construct fundamental domains for congruence subgroups of SL2(F-q[t]) and PGL(2)(F-q[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X = Xq+1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma

    KW - Groups acting on trees

    U2 - 10.1016/J.JALGEBRA.2010.08.028

    DO - 10.1016/J.JALGEBRA.2010.08.028

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    JO - Journal of Algebra

    JF - Journal of Algebra

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