Summary: A group \(G\) is called an \(\&\)-group if in \(G\setminus\{1\}\) commutativity is an equivalence relation. In this note we characterize finite \(\&\)- groups showing in particular that if \(G\) is not solvable then \(G\) is simple and isomorphic to \(\text{PSL}(2,2^n)\) for some \(n\geq 2\).