@article {
author = {Manuel Dominguez Wade, P.},
title = {$G$-Weights and $p$-Local Rank},
journal = {Journal of Algebra and Related Topics},
volume = {5},
number = {2},
pages = {1-12},
year = {2017},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2017.2711},
abstract = {Let $k$ be field of characteristic $p$, andlet $G$ be any finite group with splitting field $k$. Assume that $B$ is a $p$-block of $G$.In this paper, we introduce the notion of radical $B$-chain $C_{B}$, and we show that the $p$-local rank of $B$ is equals the length of $C_{B}$. Moreover, we prove that the vertex of a simple $kG$-module $S$ is radical if and only if it has the same vertex of the unique direct summand, up to isomorphism, of the Sylow permutationmodule whose radical quotient is isomorphic to $S$. Finally, we prove the vertices of certain direct summands of the Sylow permutation module are bounds for the vertices of simple $kG$-modules.},
keywords = {Radical vertex,$G$-weight,$p$-local rank},
url = {https://jart.guilan.ac.ir/article_2711.html},
eprint = {https://jart.guilan.ac.ir/article_2711_8f0e0342d1bad2b4ab66eb7767948d0e.pdf}
}