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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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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: http://dx.doi.org/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
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