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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On centralizers of $p$-elements in indecomposable modules


Author: Peter Landrock
Journal: Proc. Amer. Math. Soc. 82 (1981), 325-329
MSC: Primary 20C20
DOI: https://doi.org/10.1090/S0002-9939-1981-0612712-3
MathSciNet review: 612712
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Abstract: For $M$ any liftable module of a group algebra of a finite group $G$ over a field of characteristic $p$ and $x \in G$ any $p$-element, we discuss connections between the restriction of $M$ to $\left \langle x \right \rangle$ and that of $\chi$ to $\left \langle x \right \rangle$, where $\chi$ is the character of $M$. In particular we get a lower bound for the number of Jordan components of this restriction of $M$ in terms of $\chi$ restriction. For $M$ a permutation module, this bound is trivially an equality, and we derive several results by L. Scott, which hitherto have been considered relatively deep, in a very elementary and straightforward manner.


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Article copyright: © Copyright 1981 American Mathematical Society