Modular representations of finite groups with trivial restriction to Sylow subgroups

Balmer, Paul. "Modular representations of finite groups with trivial restriction to Sylow subgroups." Journal of the European Mathematical Society 015.6 (2013): 2061-2079. <http://eudml.org/doc/277548>.

@article{Balmer2013,
abstract = {Let $k$ be a field of characteristic $p$. Let $G$ be a finite group of order divisible by $p$ and $P$ a $p$-Sylow subgroup of $G$. We describe the kernel of the restriction homomorphism $T(G)\rightarrow T(P)$, for $T(−)$ the group of endotrivial representations. Our description involves functions $G\rightarrow k^\times $ that we call weak $P$-homomorphisms. These are generalizations to possibly non-normal $P\le G$ of the classical homomorphisms $G/P\rightarrow k^\times $ appearing in the normal case.},
author = {Balmer, Paul},
journal = {Journal of the European Mathematical Society},
keywords = {endotrivial module; trivial restriction to Sylow; weak homomorphism; finite groups; Sylow subgroups; stable categories; finite groups; Sylow subgroups; groups of endotrivial modules; weak homomorphisms; stable categories},
language = {eng},
number = {6},
pages = {2061-2079},
publisher = {European Mathematical Society Publishing House},
title = {Modular representations of finite groups with trivial restriction to Sylow subgroups},
url = {http://eudml.org/doc/277548},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Balmer, Paul
TI - Modular representations of finite groups with trivial restriction to Sylow subgroups
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 6
SP - 2061
EP - 2079
AB - Let $k$ be a field of characteristic $p$. Let $G$ be a finite group of order divisible by $p$ and $P$ a $p$-Sylow subgroup of $G$. We describe the kernel of the restriction homomorphism $T(G)\rightarrow T(P)$, for $T(−)$ the group of endotrivial representations. Our description involves functions $G\rightarrow k^\times $ that we call weak $P$-homomorphisms. These are generalizations to possibly non-normal $P\le G$ of the classical homomorphisms $G/P\rightarrow k^\times $ appearing in the normal case.
LA - eng
KW - endotrivial module; trivial restriction to Sylow; weak homomorphism; finite groups; Sylow subgroups; stable categories; finite groups; Sylow subgroups; groups of endotrivial modules; weak homomorphisms; stable categories
UR - http://eudml.org/doc/277548
ER -