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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
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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

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

DOI: https://doi.org/10.1090/S0002-9939-02-06506-1
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

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