DIKUL - logo
(UL)
PDF
  • Elementary abelian ▫$p$▫-groups of rank greater than or equal to ▫$4p-2$▫ are not CI-groups
    Spiga, Pablo
    We prove that an elementary abelian ▫$p$▫-group of rank ▫$4 p - 2$▫ is not a ▫$\text{CI}^{(2)}$▫-group, i.e. there exists a 2-closed transitive permutation group containing two non-conjugate regular ... elementary abelian ▫$p$▫-subgroups of rank ▫$4 p - 2$▫, see M. Hirasaka and M. Muzychuk [J. Comb. Theory, Ser. A 94, No. 2, 339-362 (2001)]. It was shown in the cited paper and by M. Muzychuk [Discrete Math. 264, No. 1-3, 167-185 (2003)] that this is related to the problem of determining whether an elementary abelian ▫$p$▫-group of rank ▫$n$▫ is a CI-group. As a strengthening of this result we prove that an elementary abelian ▫$p$▫-group ▫$E$▫ of rank greater than or equal to ▫$4 p - 2$▫ is not a CI-group, i.e. there exist two isomorphic Cayley digraphs over $E$ whose corresponding connection sets are not conjugate in ▫$\text{Aut}\,E$▫.
    Source: Journal of algebraic combinatorics. - ISSN 0925-9899 (Vol. 26, iss. 3, Nov. 2007, str. 343-355)
    Type of material - article, component part ; adult, serious
    Publish date - 2007
    Language - english
    COBISS.SI-ID - 37447939

    Link(s):

    https://doi.org/10.1007/s10801-007-0059-2
    DOI

source: Journal of algebraic combinatorics. - ISSN 0925-9899 (Vol. 26, iss. 3, Nov. 2007, str. 343-355)

loading ...
loading ...
loading ...

Shelf entry