Geodesic
A Characterization of Permutation Modules Extending a Theorem of Weiss
Documenta mathematica, Tome 25 (2020), pp. 1159-1169.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $G$ be a finite $p$-group with normal subgroup $N$. A celebrated theorem of A. Weiss gives a sufficient condition for a $\mathbb{Z}_pG$-lattice to be a permutation module, looking only at its restriction to $N$ and its $N$-fixed points. In case $N$ has order $p$, we extend the condition of Weiss to a characterization.
Classification : 20C11
Keywords: permutation modules, finite \(p\)-groups 
@article{DOCMA_2020__25__a35,
     author = {MacQuarrie, John William and Zalesskii, Pavel},
     title = {A {Characterization} of {Permutation} {Modules} {Extending} a {Theorem} of {Weiss}},
     journal = {Documenta mathematica},
     pages = {1159--1169},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a35/}
}
TY  - JOUR
AU  - MacQuarrie, John William
AU  - Zalesskii, Pavel
TI  - A Characterization of Permutation Modules Extending a Theorem of Weiss
JO  - Documenta mathematica
PY  - 2020
SP  - 1159
EP  - 1169
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a35/
LA  - en
ID  - DOCMA_2020__25__a35
ER  - 
%0 Journal Article
%A MacQuarrie, John William
%A Zalesskii, Pavel
%T A Characterization of Permutation Modules Extending a Theorem of Weiss
%J Documenta mathematica
%D 2020
%P 1159-1169
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a35/
%G en
%F DOCMA_2020__25__a35
MacQuarrie, John William; Zalesskii, Pavel. A Characterization of Permutation Modules Extending a Theorem of Weiss. Documenta mathematica, Tome 25 (2020), pp. 1159-1169. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a35/