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    A note on filled groups

    Hart, Sarah and Anabanti, Chimere (2015) A note on filled groups. Technical Report. Birkbeck College, University of London, London, UK.

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    Abstract

    Let G be a finite group and S a subset of G. Then S is product-free if S \ SS = ;, and S fills G if G� � S [ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. Street and Whitehead [J. Combin. Theory Ser. A 17 (1974), 219–226] defined a group G as filled if every locally maximal product-free set in G fills G. Street and Whitehead classified all abelian filled groups, and conjectured that the finite dihedral group of order 2n is not filled when n = 6k +1 (k � 1). The conjecture was disproved by the current authors in [Austral. Journal of Combinatorics 63 (3) (2015), 385–398], where we also classified the filled groups of odd order. This brief note completes the classification of filled dihedral groups and discusses filled groups of order up to 100.

    Metadata

    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #17
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 12 Oct 2016 12:41
    Last Modified: 22 Jul 2020 02:48
    URI: http://eprints.bbk.ac.uk/id/eprint/16182

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