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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
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.

References [Enhancements On Off] (What's this?)

  • [1] W. Feit, Representations of finite groups, Lecture Notes, Yale University, New Haven, Conn., 1969-1975.
  • [2] P. Landrock and G. O. Michler, Principal $ 2$-blocks of the simple groups of Ree type, Trans. Amer. Math. Soc. 260 (1980), 83-111. MR 570780 (81h:20013)
  • [3] L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc. 175 (1973), 101-122. MR 0310051 (46:9154)

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Article copyright: © Copyright 1981 American Mathematical Society

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