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
Full-text PDF Free Access

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?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20C15

Retrieve articles in all journals with MSC (1991): 20C15

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