Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C20

Retrieve articles in all journals with MSC: 20C20

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society