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  • On a conjecture on the permutation characters of finite primitive groups
    Spiga, Pablo
    Let ▫$G$▫ be a finite group with two primitive permutation representations on the sets ▫$\Omega_1$▫ and ▫$\Omega_2$▫ and let ▫$\pi_1$▫ and ▫$\pi_2$▫ be the corresponding permutation characters. We ... consider the case in which the set of fixed-point-free elements of ▫$G$▫ on ▫$\Omega_1$▫ coincides with the set of fixed-point-free elements of ▫$G$▫ on ▫$\Omega_2$▫, that is, for every ▫$g \in G, \pi_1(g) = 0$▫ if and only if ▫$\pi_2(g) = 0$▫. We have conjectured in Spiga ["Permutation characters and fixed-point-free elements in permutation groups", J. Algebra 299(1) (2006), 1-7] that under this hypothesis either ▫$\pi_1= \pi_2$▫ or one of ▫$\pi_1 - \pi_2$▫ and ▫$\pi_2 - \pi_1$▫ is a genuine character. In this paper we give evidence towards the veracity of this conjecture when the socle of ▫$G$▫ is a sporadic simple group or an alternating group. In particular, the conjecture is reduced to the case of almost simple groups of Lie type.
    Source: Bulletin of the Australian Mathematical Society. - ISSN 0004-9727 (Vol. 102, iss. 1, Aug. 2020, str. 77-90)
    Type of material - article, component part ; adult, serious
    Publish date - 2020
    Language - english
    COBISS.SI-ID - 28285699

    Link(s):

    https://doi.org/10.1017/S0004972719001060
    DOI

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