×

zbMATH — the first resource for mathematics

Endliche auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind. (Finite solvable groups all whose character degrees are prime powers). (German) Zbl 0596.20007
This paper is part of the author’s dissertation ”Endliche Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind” (Universität Mainz, 1984), which was reviewed in Zbl 0542.20003. Note that the paper under review consists of the first seven chapters of that dissertation. The remaining (eighth) chapter of it is the paper ”Endliche nicht- auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind” [in J. Algebra 96, 114-119 (1985)] which was reviewed in Zbl 0567.20004.
Reviewer: R.W.van der Waall

MSC:
20C15 Ordinary representations and characters
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Berger, T.R, Characters and derived length in groups of odd order, J. algebra, 39, 199-207, (1976) · Zbl 0362.20012
[2] Dornhoff, L, Group representation theory (parts A, B), (1971/1972), Dekker New York · Zbl 0236.20004
[3] Feit, W, The representation theory of finite groups, (1982), North-Holland Amsterdam/New York/Oxford · Zbl 0493.20007
[4] Garrison, S, On groups with a small number of character degrees, ()
[5] Hall, P; Higman, G, The p-length of a p-soluble group and reduction theorems for Burnside’s problem, (), 1-42, No. 6 · Zbl 0073.25503
[6] Huppert, B, Darstellungstheorie endlicher gruppen, (1973/1974), Universität Mainz, Skript
[7] Huppert, B, Endliche gruppen I, (1979), Springer-Verlag Berlin/Heidelberg/New York · Zbl 0412.20002
[8] Huppert, B; Blackburn, N, Finite groups II, III, (1982), Springer-Verlag Berlin/Heidelberg/New York · Zbl 0514.20002
[9] Isaacs, I.M, Character theory of finite groups, (1976), Academic Press New York/San Francisco/London · Zbl 0337.20005
[10] Isaacs, I.M, Finite groups with small character degrees and large prime divisors, I, Pacific J. math., 23, 273-280, (1967) · Zbl 0178.02203
[11] Isaacs, I.M, Groups having at most three irreducible character degrees, (), 185-188 · Zbl 0172.03401
[12] Isaacs, I.M, Characters of solvable and symplectic groups, Amer. J. math., 95, 594-653, (1973) · Zbl 0277.20008
[13] Isaacs, I.M, Character degrees and derived length of a solvable group, Canad. J. math., 27, 146-151, (1975) · Zbl 0306.20008
[14] Isaacs, I.M; Passman, D.S, Groups whose irreducible representations have degrees dividing pe, Illinois J. math., 8, 446-457, (1964) · Zbl 0199.06303
[15] Isaacs, I.M; Passman, D.S, A characterization of groups in terms of the degrees of their characters, I, Pacific J. math., 15, 877-903, (1965) · Zbl 0132.01902
[16] Isaacs, I.M; Passman, D.S, A characterization of groups in terms of the degrees of their characters, II, Pacific J. math., 24, 467-510, (1968) · Zbl 0155.05502
[17] Isaacs, I.M; Passman, D.S, Finite groups with small character degrees and large prime divisors, II, Pacific J. math., 29, 311-324, (1969) · Zbl 0177.04402
[18] Kurzweil, H, Endliche gruppen, (1977), Springer-Verlag Berlin/Heidelberg/New York · Zbl 0381.20001
[19] Passman, D.S, Groups whose irreducible representations have degrees dividing p2, Pacific J. math., 17, 475-496, (1966) · Zbl 0145.03005
[20] Seitz, G.M, M-groups and the supersolvable residual, Math. Z., 110, 101-122, (1969) · Zbl 0214.04303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.