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    Groups containing small locally maximal product-free sets

    Hart, Sarah and Anabanti, Chimere (2016) Groups containing small locally maximal product-free sets. International Journal of Combinatorics , p. 8939182. ISSN 1687-9163.

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    Abstract

    Let G be a group, and S a non-empty subset of G. Then S is product-free if ab is not in S for all a, b in S. We say S is locally maximal product-free if S is product-free and not properly contained in any other product-free set. A natural question is to determine the smallest possible size of a locally maximal product-free set in G. Alternatively, given a positive integer k, one can ask: what is the largest integer n_k such that there is a group of order n_k with a locally maximal product-free set of size k? The groups containing locally maximal product-free sets of sizes 1 and 2 are known, and it has been conjectured that n_3 = 24. The purpose of this paper is to prove this conjecture and hence show that the list of known locally maximal product-free sets of size 3 is complete. We also report some experimental observations about the sequence n_k.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 07 Oct 2016 14:54
    Last Modified: 20 Jan 2017 10:49
    URI: http://eprints.bbk.ac.uk/id/eprint/16146

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