On a result of M. Suzuki (Q1924894)

In 1950 \textit{L. Rédei} proved [J. Reine Angew. Math. 188, 201-227 (1950; Zbl 0040.29902)], that \(A_5\) is the unique simple group of even order which is non-abelian but each of its nonmaximal proper subgroups is abelian. Seven years later \textit{M. Suzuki} observed [Proc. Am. Math. Soc. 8, 626-695 (1957; Zbl 0079.03104)], that this characterization of \(A_5\) remains valid if we take nilpotency in place of abelity. Our paper contains an even stronger characterization of \(A_5\), namely \(A_5\) is the unique simple group of even order with the property that each nonmaximal proper subgroup is weakly 2-closed in it. The proof is short and elementary.