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A characteristic subgroup and kernels of Brauer characters

Published online by Cambridge University Press:  17 April 2009

I. M. Isaacs  and
Gabriel Navarro
I. M. Isaacs
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States of America e-mail: isaacs@math.wisc.edu
Gabriel Navarro
Affiliation:
Facultat de Matemàtiques, Universitat de València, Burjassot, València 46100, Spain e-mail: gabriel@uv.es
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If G is finite group and P is a Sylow p-subgroup of G, we prove that there is a unique largest normal subgroup L of G such that L ⋂ P = L ⋂ NG (P). If G is p-solvable, then L is the intersection of the kernels of the irreducible Brauer characters of G of degree not divisible by p.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 381 - 384
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Gajendragadkar, D., ‘A characteristic class of characters of finite π-separable groups,’ J. Algebra 59 (1979), 237–259.CrossRefGoogle Scholar
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[3]Isaacs, I.M., Character theory of finite groups (Dover Publication, New York, 1994).Google Scholar
[4]Navarro, G., ‘A new character correspondence in groups of odd order,’ J. Algebra 268 (2003), 8–21.CrossRefGoogle Scholar