Solvable groups having only three rational classes of 2-elements. (Q641813)

A result by \textit{A. Moretó} and \textit{G. Navarro} [Isr. J. Math. 163, 85-92 (2008; Zbl 1152.20011)] implies that if the number of real conjugacy classes of a finite group \(G\) is at most three, then \(G\) is solvable with 2-length at most 1. The paper under review shows that under the additional hypothesis that \(G\) is solvable, the conclusion remains true under the much weaker hypothesis that \(G\) has at most three rational conjugacy classes.