Degrees, kernels and quasikernels of monolithic characters
Proc. Amer. Math. Soc. 128 (2000), 3211-3219
May 11, 2000
Full-text PDF Free Access
Similar Articles |
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.
Berkovich, On Isaacs’ three character
degrees theorem, Proc. Amer. Math. Soc.
125 (1997), no. 3,
669–677. MR 1376750
Y. Berkovich, I. M. Isaacs and L. Kazarin, Distinct monolithic character degrees, J. Algebra 216 (1999), 448-480.
G. Berkovich and E.
M. Zhmud′, Characters of finite groups. Part 1,
Translations of Mathematical Monographs, vol. 172, American
Mathematical Society, Providence, RI, 1998. Translated from the Russian
manuscript by P. Shumyatsky [P. V. Shumyatskiĭ] and V. Zobina. MR 1486039
H. Conway, R.
T. Curtis, S.
P. Norton, R.
A. Parker, and R.
A. Wilson, Atlas of finite groups, Oxford University Press,
Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups;
With computational assistance from J. G. Thackray. MR 827219
Martin Isaacs, Character theory of finite groups, Academic
Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure
and Applied Mathematics, No. 69. MR 0460423
Willems, Blocks of defect zero in finite simple groups of Lie
type, J. Algebra 113 (1988), no. 2,
929777 (89c:20025), http://dx.doi.org/10.1016/0021-8693(88)90176-7
- Y. Berkovich, On Isaacs' three character degrees theorem, Proc. Amer. Math. Soc. 125, 3 (1997), 669-677. MR 97i:20006
- Y. Berkovich, I. M. Isaacs and L. Kazarin, Distinct monolithic character degrees, J. Algebra 216 (1999), 448-480.
- 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
- 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.M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. MR 57:417
- W. Willems, Blocks of defect zero in finite simple groups, J. of Algebra 113 (1988), 511-522. MR 89c:20025
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (1991):
Retrieve articles in all journals
with MSC (1991):
Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
$\pi$-closed and $\pi$-nilpotent groups,
kernel and quasikernel,
classification of finite simple groups
Received by editor(s):
January 21, 1999
May 11, 2000
The author was supported in part by the Ministry of Absorption of Israel.
Ronald M. Solomon
© Copyright 2000
American Mathematical Society