On centralizers of $p$-elements in indecomposable modules
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- by Peter Landrock PDF
- Proc. Amer. Math. Soc. 82 (1981), 325-329 Request permission
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
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W. Feit, Representations of finite groups, Lecture Notes, Yale University, New Haven, Conn., 1969-1975.
- Peter Landrock and Gerhard O. Michler, Principal $2$-blocks of the simple groups of Ree type, Trans. Amer. Math. Soc. 260 (1980), no. 1, 83–111. MR 570780, DOI 10.1090/S0002-9947-1980-0570780-5
- L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc. 175 (1973), 101–121. MR 310051, DOI 10.1090/S0002-9947-1973-0310051-1
Additional Information
- © Copyright 1981 American Mathematical Society
- 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