A generalization of a result of Hegedüs

A famous result of P. Hegedüs describes the structure of finite rational $\{2,5\}$-groups. In this paper, we show how Hegedüs’ proof can be used to obtain a similar result for the more general situation of a finite rational $2$-group acting faithfully and with the eigenvector property on a f.d ${\mathbb{F}}_p$-vector space with $p\ge 5$.