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Endliche nicht-auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind. (German) Zbl 0567.20004
In a previous paper the author has classified all those solvable finite groups whose degrees of all the complex irreducible representations are prime powers [see J. Algebra 94, 211-255 (1985)]. Here the work is finished in that it is proved that if the Brauer height conjecture is true, the non-solvable group G has all its irreducible complex representations of prime power degree if and only if \(G=B\times Y\), where B is Abelian, \(Y\cong PSL(2,4)\) or \(Y\cong PSL(2,8)\).
Reviewer: R.W.van der Waall

20C15 Ordinary representations and characters
20D05 Finite simple groups and their classification
Full Text: DOI
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