DIKUL - logo
(UL)
  • Regular maps with nilpotent automorphism groups
    Malnič, Aleksander ; Nedela, Roman ; Škoviera, Martin
    We study regular maps with nilpotent automorphism groups in detail. We prove that every nilpotent regular map decomposes into a direct product of maps ▫$\mathscr{H} \times \mathscr{K}$▫, where ... ▫${\text Aut}(\mathscr{H})$▫ is a 2-group and ▫$\mathscr{K}$▫ is a map with a single vertex and an odd number of semiedges. Many important properties of nilpotent maps follow from this canonical decomposition, including restrictions on the valency, covalency, and the number of edges. We also show that, apart from two well-defined classes of maps on at most two vertices and their duals, every nilpotent regular map has both its valency and covalency divisible by 4. Finally, we give a complete classification of nilpotent regular maps of nilpotency class 2.
    Vir: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 33, iss. 8, 2012, str. 1974-1986)
    Vrsta gradiva - članek, sestavni del
    Leto - 2012
    Jezik - angleški
    COBISS.SI-ID - 16581721

    Povezava(-e):

    http://dx.doi.org/10.1016/j.ejc.2012.06.001

Vnos na polico