On $B_5$-Groups

Abstract

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