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  • Finite groups admitting an oriented regular representation
    Spiga, Pablo
    In this paper, we investigate finite groups admitting an oriented regular representation and we give a partial answer to a 1980 question of Lazslo Babai: "Which [finite] groups admit an oriented ... graph as a DRR?" It is easy to see and well-understood that generalised dihedral groups do not admit ORRs. We prove that, apart from ▫$C_3^2$▫ and ▫$C_3 \times C_2^3$▫, every finite group, which is neither a generalised dihedral group nor a 2-group, has an ORR. In particular, the classification of the finite groups admitting an ORR is reduced to the class of 2-groups. We also give strong structural conditions on finite 2-groups not admitting an ORR. Finally, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting an ORR.
    Source: Journal of combinatorial theory. Series A. - ISSN 0097-3165 (Vol. 153, Jan. 2018, str. 76-97)
    Type of material - article, component part ; adult, serious
    Publish date - 2018
    Language - english
    COBISS.SI-ID - 18631257

    Link(s):

    https://doi.org/10.1016/j.jcta.2017.08.001
    DOI

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