Finite solvable groups with at most two nonlinear irreducible characters of each degree. (English) Zbl 1162.20007
In earlier work, Y. Berkovich has characterized the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity 1 [J. Algebra 184, No. 2, 584-603 (1996; Zbl 0861.20008)], and Y. Berkovich, D. Chillag and M. Herzog have described in detail the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity 1 except for possibly one which has multiplicity 2 [Proc. Am. Math. Soc. 115, No. 4, 955-959 (1992; Zbl 0822.20004)].
In the paper under review the authors use these results to give a detailed description of the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity not exceeding 2. The list is too long to be stated here in detail, and the proof is quite technical.
In the paper under review the authors use these results to give a detailed description of the finite solvable groups all of whose nonlinear irreducible character degrees have multiplicity not exceeding 2. The list is too long to be stated here in detail, and the proof is quite technical.
Reviewer: Thomas Michael Keller (San Marcos)
MSC:
| 20C15 | Ordinary representations and characters |
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
Keywords:
finite solvable groups; multiplicities of character degrees; nonlinear irreducible charactersReferences:
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