Abstract
Let G be a group and S a non-empty subset of G. If ab /∈ S for any a, b ∈ S, then Sis called sum-free. We show that if S is maximal by inclusion and no proper subsetgenerates hSi then |S| ≤ 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 ∈ S such thata /∈ hS \ {a}i.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Journal | Electronic Journal of Combinatorics |
| Volume | 16 |
| Issue number | 1 |
| Publication status | Published - 2009 |
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Giudici, M., & Hart, S. (2009). Small maximal sum-free sets. Electronic Journal of Combinatorics, 16(1), 1-17.