On strongly sum-free subsets of abelian groups

In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists ${\displaystyle n_0=n_0\left(l\right)}$ with the following property: for every ${\displaystyle n\ge n_0}$ and any n elements ${\displaystyle a_1,...,a_n}$ of a group such that the product of any two of them is different from the unit element of the group, there exist l of the ${\displaystyle a_i}$ such that ${\displaystyle a_{i_j}{a}_{i_k}\ne a_m}$ for ${\displaystyle 1\le j<k\le l}$ and ${\displaystyle 1\le m\le n}$. In this note we answer this question in the affirmative in the first non-trivial case when l=3 and the group is abelian, proving the following result.