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  • The symmetric genus spectrum of finite groups
    Conder, Marston D. E. ; Tucker, Thomas W.
    The symmetric genus of the finite group ▫$G$▫, denoted by ▫$\sigma(G)$▫, is the smallest non-negative integer ▫$g$▫ such that the group ▫$G$▫ acts faithfully on a closed orientable surface of genus ... ▫$g$▫ (not necessarily preserving orientation). This paper investigates the question of whether for every non-negative integer ▫$g$▫, there exists some ▫$G$▫ with symmetric genus ▫$g$▫. It is shown that that the spectrum (range of values) of ▫$\sigma$▫ includes every non-negative integer ▫$g \not\equiv 8$▫ or ▫$14 \bmod 18$▫, and moreover, if a gap occurs at some ▫$g \equiv 8$▫ or ▫$14 \bmod 18$▫, then the prime-power factorization of ▫$g - 1$▫ includes some factor ▫$p^e \equiv 5 \mod 6$▫. In fact, evidence suggests that this spectrum has no gaps at all.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 2, 2011, str. 271-289)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16267609

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/127
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 2, 2011, str. 271-289)

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