Degree-problems. I: Squarefree character degrees (Q1063680)

Let \(G\) be a finite group with the property that all its irreducible complex characters have squarefree degrees. The authors show that in the case of \(G\) being solvable there are universal bounds for the derived length and the nilpotent length of \(G\), which are 4 and 3, respectively; if \(G\) is nonsolvable they show that \(G\) is the direct product of the alternating group \(A_7\) and a solvable group \(N\).