A block theoretic analogue of a theorem of Glauberman and Thompson
Authors:
Radha Kessar and Markus Linckelmann
Journal:
Proc. Amer. Math. Soc. 131 (2003), 35-40
MSC (2000):
Primary 20C20
DOI:
https://doi.org/10.1090/S0002-9939-02-06506-1
Published electronically:
May 13, 2002
MathSciNet review:
1929020
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: If $p$ is an odd prime, $G$ a finite group and $P$ a Sylow-$p$-subgroup of $G$, a theorem of Glauberman and Thompson states that $G$ is $p$-nilpotent if and only if $N_{G}(Z(J(P)))$ is $p$-nilpotent, where $J(P)$ is the Thompson subgroup of $P$ generated by all abelian subgroups of $P$ of maximal order. Following a suggestion of G. R. Robinson, we prove a block-theoretic analogue of this theorem.
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Additional Information
Radha Kessar
Affiliation:
Department of Mathematics, University College, High Street, Oxford OX14BH, United Kingdom
Address at time of publication:
Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210
MR Author ID:
614227
Markus Linckelmann
Affiliation:
CNRS, Université Paris 7, UFR Mathématiques, 2, place Jussieu, 75251 Paris Cedex 05, France
Address at time of publication:
Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210
MR Author ID:
240411
Received by editor(s):
June 14, 2001
Received by editor(s) in revised form:
August 15, 2001
Published electronically:
May 13, 2002
Communicated by:
Stephen D. Smith
Article copyright:
© Copyright 2002
American Mathematical Society
