On \(B_5\)-Groups

Abstract

A group \(G\) is said to be a \(B_k\)-group if for any \(k\)-subset \(\{a_1, \ldots, a_k\}\) of \(G\), \(\left|\{a_ia_j \mid 1 \leq i, j \leq k\}\right| \leq \frac{k(k+1)}{2}\). In this paper, a complete classification of \(B_5\)-groups is given.