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  • Regular Cayley maps on dihedral groups with the smallest kernel
    Kovács, István, 1969- ; Kwon, Young Soo
    Let ▫$\mathcal{M} = \mathrm{CM}(D_n,X,p)$▫ be a regular Cayley map on the dihedral group ▫$D_n$▫ of order ▫$2n, n \ge 2,$▫ and let ▫$\psi$▫ be the power function associated with ▫$\mathcal{M}$▫. In ... this paper it is shown that the kernel ▫$\mathrm{Ker}(\psi)$▫ of the skew-morphism ▫$\psi$▫ is a dihedral subgroup of ▫$D_n$▫ and if ▫$n \ne 3,$▫ then the kernel ▫$\mathrm{Ker}(\psi)$▫ is of order at least ▫$4$▫. Moreover, all $\math▫cal{M}$▫ are classified for which ▫$\mathrm{Ker}(\psi)$▫ is of order ▫$4$▫. In particular, besides ▫$4$▫ sporadic maps on ▫$4,4,8$▫ and ▫$12$▫ vertices respectively, two infinite families of non-▫$t$▫-balanced Cayley maps on ▫$D_n$▫ are obtained.
    Vir: Journal of algebraic combinatorics. - ISSN 0925-9899 (Vol. 44, iss. 4, 2016, str. 831-847)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 1538922180

    Povezava(-e):

    http://dx.doi.org/10.11007/s10801-016-0689-3

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