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Degrees, kernels and quasikernels of monolithic characters

Author: Yakov Berkovich
Journal: Proc. Amer. Math. Soc. 128 (2000), 3211-3219
MSC (1991): Primary 20C15
Published electronically: May 11, 2000
MathSciNet review: 1707506
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Abstract | References | Similar Articles | Additional Information

Abstract: Theorem 5 yields the condition sufficient for a group to be a direct product of a $\pi $-group and an abelian $\pi '$-group. We also obtain characterizations of nilpotent groups, prime power groups, $p$-nilpotent and $p$-closed groups in the language of characters. Proofs of some results depend on the classification of finite simple groups. Some problems are posed and discussed.

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

  • [B] Y. Berkovich, On Isaacs' three character degrees theorem, Proc. Amer. Math. Soc. 125, 3 (1997), 669-677. MR 97i:20006
  • [BIK] Y. Berkovich, I. M. Isaacs and L. Kazarin, Distinct monolithic character degrees, J. Algebra 216 (1999), 448-480.
  • [BZ] Y. G. Berkovich and E.M. Zhmud', Characters of Finite Groups. Parts 1, 2, Translations of Mathematical Monographs 172, 181, American Mathematical Society, Providence, 1998. MR 98m:20011
  • [CCNPW] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985. MR 88g:20025
  • [I] I.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. MR 57:417
  • [W] W. Willems, Blocks of defect zero in finite simple groups, J. of Algebra 113 (1988), 511-522. MR 89c:20025

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Additional Information

Yakov Berkovich
Affiliation: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Keywords: $\pi$-closed and $\pi$-nilpotent groups, kernel and quasikernel, monolithic character, Frobenius group, classification of finite simple groups
Received by editor(s): January 21, 1999
Published electronically: May 11, 2000
Additional Notes: The author was supported in part by the Ministry of Absorption of Israel.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society

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