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Proceedings of the American Mathematical Society
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
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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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612712-3
PII: S 0002-9939(1981)0612712-3
Article copyright: © Copyright 1981 American Mathematical Society