@article {IsNa2005,
 author="I.M. Isaacs and Gabriel Navarro",
 title={A characteristic subgroup and kernels of Brauer characters},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="3",
 pages="381--384",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="8th June, 2005",
 classmath="20D20",
 publisher={AMPAI, Australian Mathematical Society},
 url="http://www.austms.org.au/Publ/Bulletin/V72P3/723-5179-IsNa/index.shtml",
 acknowledgement={The second author is partially supported by the Ministerio de Educaci\'on 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 $L\cap P=L\cap {\bf N}_G (P)$. 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 $p$. }
}