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    Groups whose locally maximal product-free sets are complete

    Anabanti, Chimere and Erskine, G. and Hart, Sarah B. (2016) Groups whose locally maximal product-free sets are complete. Working Paper. Birkbeck, 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 complete if G� � S [ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. If S is product-free and complete then S is locally maximal, but the converse does not necessarily hold. Street and Whitehead [11] defined a group G as filled if every locally maximal product-free set S in G is complete (the term comes from their use of the phrase ‘S fills G’ to mean S is complete). They 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 two of the current authors in [2], where we also classified the filled groups of odd order. In this paper we classify filled dihedral groups, filled nilpotent groups and filled groups of order 2np where p is an odd prime. We use these results to determine all filled groups of order up to 2000.

    Metadata

    Item Type: Monograph (Working Paper)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #25
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Research Centre: Applied Macroeconomics, Birkbeck Centre for
    Depositing User: Administrator
    Date Deposited: 22 Mar 2019 13:17
    Last Modified: 27 Jul 2019 15:20
    URI: http://eprints.bbk.ac.uk/id/eprint/26751

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