# Small maximal sum-free sets

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

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SmallCFSF5.pdf

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 $a \notin \langle S \setminus \{a\}\rangle$.