Geodesic
Small maximal sum-free sets.
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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Let $G$ be a group and $S$ a non-empty subset of $G$. If $ab \notin S$ for any $a, b \in S$, then $S$ is called sum-free. We show that if $S$ is maximal by inclusion and no proper subset generates $\langle S\rangle$ 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 $a \notin \langle S \setminus \{a\}\rangle$.
DOI : 10.37236/148
Classification : 20D60, 11B75, 20F05
Mots-clés : maximal sum-free sets 
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     author = {Michael Giudici and Sarah Hart},
     title = {Small maximal sum-free sets.},
     journal = {The electronic journal of combinatorics},
     year = {2009},
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     number = {1},
     doi = {10.37236/148},
     zbl = {1168.20009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/148/}
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Michael Giudici; Sarah Hart. Small maximal sum-free sets.. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/148

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