Degrees, kernels and quasikernels of monolithic characters

Author:
Yakov Berkovich

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3211-3219

MSC (1991):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-00-05550-7

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 -group and an abelian -group. We also obtain characterizations of nilpotent groups, prime power groups, -nilpotent and -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.

**[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

Email:
berkov@mathcs2.haifa.ac.il

DOI:
https://doi.org/10.1090/S0002-9939-00-05550-7

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