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    Locally maximal product-free sets of size 3

    Hart, Sarah B. and Anabanti, Chimere (2015) Locally maximal product-free sets of size 3. Working Paper. Birkbeck College, University of London, London, UK.

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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 =2 S for all a; b 2 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 what is the smallest possible size of a locally maximal product-free set in G. The groups containing locally maximal product-free sets of sizes 1 and 2 were classi�ed in [3]. In this paper, we prove a conjecture of Giudici and Hart in [3] by showing that if S is a locally maximal product-free set of size 3 in a group G, then jGj � 24. This shows that the list of known locally maximal product-free sets given in [3] is complete.

    Metadata

    Item Type: Monograph (Working Paper)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #10
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hart
    Date Deposited: 12 Oct 2016 12:42
    Last Modified: 03 Apr 2019 09:57
    URI: http://eprints.bbk.ac.uk/id/eprint/16181

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