Degree-problems I squarefree character degrees
Copyright policy )Degree-problems I squarefree character degrees
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 \(N\).
squarefree degrees, Ordinary representations and characters, irreducible complex characters, nilpotent length, derived length, Finite simple groups and their classification, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Arithmetic and combinatorial problems involving abstract finite groups
squarefree degrees, Ordinary representations and characters, irreducible complex characters, nilpotent length, derived length, Finite simple groups and their classification, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Arithmetic and combinatorial problems involving abstract finite groups
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