On strongly sum-free subsets of abelian groups

• Autorzy: Tomasz Łuczak , Tomasz Schoen
• Języki publikacji: EN

Abstrakty

EN

In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists $n_0 = n_0(l)$ with the following property: for every $n ≥ n_0$ and any n elements $a_1,...,a_n$ 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 $a_i$ such that $a_{i_j}a_{i_k} ≠ a_m$ for $1 ≤ j < k ≤ l$ and $1 ≤ m ≤ n$. 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 71
• Numer: 1
• Strony: 149-151

Daty

wydano

1996

otrzymano

1995-11-03

poprawiono

1996-01-09

Twórcy

autor

Tomasz Łuczak

• Department of Discrete Mathematics Adam Mickiewicz University 60-769 Poznań, Poland

autor

Tomasz Schoen

• Department of Discrete Mathematics Adam Mickiewicz University 60-769 Poznań, Poland

Bibliografia

• [1] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1994, Problem C14.