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Degrees, kernels and quasikernels of monolithic characters
Author(s):
Yakov
Berkovich
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3211-3219.
MSC (1991):
Primary 20C15
Posted:
May 11, 2000
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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.
References:
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- [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:
10.1090/S0002-9939-00-05550-7
PII:
S 0002-9939(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
Posted:
May 11, 2000
Additional Notes:
The author was supported in part by the Ministry of Absorption of Israel.
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
2000,
American Mathematical Society
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