A characteristic subgroup and kernels of Brauer characters

Bulletin of the Australian Mathematical Society Bull. Austral. Math. Soc. 0004-9727 ALNBAB 2005 72 3 10.wxyz/CV72P3 http://www.austms.org.au/Publ/Bulletin/V72P3/ A characteristic subgroup and kernels of Brauer characters I.M. Isaacs Gabriel Navarro 13 February 2006 2006 2 13 381 384 723-5179-IsNa-2005 10.wxyz/C2005V72P3p381 http://www.austms.org.au/Publ/Bulletin/V72P3/723-5179-IsNa/ 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 $p$. 20D20 The second author is partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01. D. Gajendragadkar A characteristic class of characters of finite π -separable groups J. Algebra D. Gajendragadkar; A characteristic class of characters of finite $\pi $-separable groups, \textit{J. Algebra} \textbf{59} (1979), pp.~237--259. I.M. Isaacs Characters of π -separable groups J. Algebra I.M. Isaacs; Characters of $\pi $-separable groups, \textit{J. Algebra} \textbf{86} (1984), pp.~98--112. I.M. Isaacs Character theory of finite groups Dover Publication I.M. Isaacs; \textit{Character theory of finite groups} (Dover Publication, New York, 1994). G. Navarro A new character correspondence in groups of odd order J. Algebra G. Navarro; A new character correspondence in groups of odd order, \textit{J. Algebra} \textbf{268} (2003), pp.~8--21.