Add to ORKGLet G be a group and S a non-empty subset of G. If ab∉S for any a,b∈S, then S is called sum-free. We show that if S is maximal by inclusion and no proper subset generates ⟨S⟩ 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 that a∉⟨S∖{a}⟩
Let G be a finite group and S a subset of G. Then S is product-free if S ∩ SS = ∅, and complete if G...
A subset S of a group G is said to be a sum-free set if S ∩ (S + S) = {circled division slash}. Such...
Let S be a non-empty subset of a group G. We say S is product-free if S contains no solutions to ab=...
Let G be a group and S a non-empty subset of G. If ab / ∈ S for any a, b ∈ S, then S is called sum-f...
Let G be a group, and S a non-empty subset of G. Then S is product-free if ab is not in S for all a,...
Let G be a finite group, and S a sum-free subset of G. The set S is locally maximal in G if\ud S is ...
AbstractA subset S of a group G is said to be a sum-free set if S ∩ (S + S) = ⊘. Such a set is maxim...
We recently answered the three questions of Bertram in the finite abelian case. In this paper, we\ud...
AbstractWe show that the number of maximal sum-free subsets of {1,2,…,n} is at most 23n/8+o(n). We a...
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...
Every locally maximal product-free set S in a finite group G satisfies G = S[SS[S−1S[ SS−1 [pS, wher...
Cameron and Erdős [6] asked whether the number of maximal sum-free sets in { 1 , . . . , n } is much...
We give a brief survey on sum-free subsets of the natural numbers, highlighting recent results which...
A subset S of an additive group G is called a maximal sum-free set in G if (S+S) [formula omitted] S...
Let A be a subset of an abelian group G. We say that A is sum-free if there do not exist x,y and z i...
Let G be a finite group and S a subset of G. Then S is product-free if S ∩ SS = ∅, and complete if G...
A subset S of a group G is said to be a sum-free set if S ∩ (S + S) = {circled division slash}. Such...
Let S be a non-empty subset of a group G. We say S is product-free if S contains no solutions to ab=...
Let G be a group and S a non-empty subset of G. If ab / ∈ S for any a, b ∈ S, then S is called sum-f...
Let G be a group, and S a non-empty subset of G. Then S is product-free if ab is not in S for all a,...
Let G be a finite group, and S a sum-free subset of G. The set S is locally maximal in G if\ud S is ...
AbstractA subset S of a group G is said to be a sum-free set if S ∩ (S + S) = ⊘. Such a set is maxim...
We recently answered the three questions of Bertram in the finite abelian case. In this paper, we\ud...
AbstractWe show that the number of maximal sum-free subsets of {1,2,…,n} is at most 23n/8+o(n). We a...
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...
Every locally maximal product-free set S in a finite group G satisfies G = S[SS[S−1S[ SS−1 [pS, wher...
Cameron and Erdős [6] asked whether the number of maximal sum-free sets in { 1 , . . . , n } is much...
We give a brief survey on sum-free subsets of the natural numbers, highlighting recent results which...
A subset S of an additive group G is called a maximal sum-free set in G if (S+S) [formula omitted] S...
Let A be a subset of an abelian group G. We say that A is sum-free if there do not exist x,y and z i...
Let G be a finite group and S a subset of G. Then S is product-free if S ∩ SS = ∅, and complete if G...
A subset S of a group G is said to be a sum-free set if S ∩ (S + S) = {circled division slash}. Such...
Let S be a non-empty subset of a group G. We say S is product-free if S contains no solutions to ab=...