*Bull. Austral. Math. Soc.* 72(3) pp.381--384, 2005.

# A characteristic subgroup and kernels of

Brauer characters

## I.M. Isaacs |
## Gabriel Navarro |

The second author is partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01.

## Abstract

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*(*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*.#### Click to download PDF of this article (free access until July 2006)

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(Metadata: XML, RSS, BibTeX) | MathSciNet: MR2199639 | Z'blatt-MATH: 1096.20013 |

## References

- D. Gajendragadkar;

A characteristic class of characters of finite*π*-separable groups,

*J. Algebra***59**(1979), pp. 237--259.**MR543247** - I.M. Isaacs;

Characters of*π*-separable groups,

*J. Algebra***86**(1984), pp. 98--112.**MR727371** - I.M. Isaacs;

*Character theory of finite groups*(Dover Publication, New York, 1994).**MR1280461** - G. Navarro;

A new character correspondence in groups of odd order,

*J. Algebra***268**(2003), pp. 8--21.**MR2004477**

ISSN 0004-9727