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Proceedings of the American Mathematical Society

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Primes dividing character degrees and character orbit sizes


Author: David Gluck
Journal: Proc. Amer. Math. Soc. 101 (1987), 219-225
MSC: Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-1987-0902531-8
MathSciNet review: 902531
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Abstract: We consider an abelian group $ A$ which acts faithfully and coprimely on a solvable group $ G$. We show that some $ A$-orbit on $ \operatorname{Irr}(G)$ must have cardinality divisible by almost half the primes in $ \pi (A)$. As a corollary, we improve a recent result of I. M. Isaacs concerning the maximum number of primes dividing any one character degree of a solvable group.


References [Enhancements On Off] (What's this?)

  • [1] D. Gluck, Trivial set-stabilizers in finite permutation groups, Canad. J. Math. 35 (1983), 59-67. MR 685817 (84c:20008)
  • [2] D. Gluck and T. R. Wolf, Defect groups and character heights in blocks of solvable groups. II, J. Algebra 87 (1984), 222-246. MR 736777 (85c:20008)
  • [3] B. Huppert, Endliche Gruppen, Springer-Verlag, Berlin, 1967. MR 0224703 (37:302)
  • [4] I. M. Isaacs, Character theory of finite groups, Academic Press, New York, 1976. MR 0460423 (57:417)
  • [5] -, Solvable group character degrees and sets of primes, J. Algebra 104 (1986), 209-230. MR 866771 (87m:20026)
  • [6] T. R. Wolf, Defect groups and character heights in blocks of solvable groups, J. Algebra 72 (1981), 183-209. MR 634622 (83d:20009)
  • [7] -, Solvable and nilpotent subgroups of $ \operatorname{GL}(n,{q^m})$, Canad. J. Math. 34 (1982), 1097-1111. MR 675682 (84b:20057)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0902531-8
Article copyright: © Copyright 1987 American Mathematical Society

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