Small maximal sum-free sets

Guidici, M and Hart, S (2006) Small maximal sum-free sets. (submitted for publication) , (Submitted)

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Abstract

Let $G$ be a group and $S \subseteq G$. If $xy \notin S$ for any $x,y\in S$, then $S$ is called \emph{sum-free}. We show that if $S$ is maximal by inclusion and no proper subset generates $\la S\ra$ then $|S|\leq 2$. We determine all groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists $a \in S$ such that $a \notin \langle S \setminus \{a\}\rangle$.

Item Type:	Article
Additional Information:	This is a pre-print.
Keyword(s) / Subject(s):	sum-free sets, groups
School or Research Centre:	Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User:	Sarah Hart
Date Deposited:	10 Jan 2007
Last Modified:	17 Apr 2013 12:33
URI:	http://eprints.bbk.ac.uk/id/eprint/439

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• Small maximal sum-free sets. (deposited 10 Jan 2007) [Currently Displayed]
  • Small maximal sum-free sets. (deposited 03 Nov 2009 17:32)

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