Comptes Rendus
Group theory
A new canonical induction formula for p-permutation modules
Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 327-332.

Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any p-permutation module as a Z[1/p]-linear combination of modules induced and inflated from projective modules associated with subquotient groups. The underlying constructions include, for any given finite group, a ring with a Z-basis indexed by conjugacy classes of triples (U,K,E) where U is a subgroup, K is a p-residue-free normal subgroup of U, and E is an indecomposable projective module of the group algebra of U/K.

En application de la théorie de l'induction canonique de Robert Boltje, nous présentons une formule stable par restriction au moyen de laquelle tout module de p-permutation est exprimé sous forme de combinaison Z[1/p]-linéaire des inductions des inflations des modules projectifs associés à des groupes de sous-quotients. Les constructions concernées comprennent, pour tout groupe fini, un anneau qui a une Z-base indexée par les classes de conjugaison des triplets (U,K,E) avec U un sous-groupe, Op(K)=KU et E un module projectif indécomposable de l'algèbre de groupe de U/K.

Published online:
DOI: 10.1016/j.crma.2019.04.004

Laurence Barker 1; Hatice Mutlu 1

1 Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
     author = {Laurence Barker and Hatice Mutlu},
     title = {A new canonical induction formula for \protect\emph{p}-permutation modules},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {327--332},
     publisher = {Elsevier},
     volume = {357},
     number = {4},
     year = {2019},
     doi = {10.1016/j.crma.2019.04.004},
     language = {en},
AU  - Laurence Barker
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PB  - Elsevier
DO  - 10.1016/j.crma.2019.04.004
LA  - en
ID  - CRMATH_2019__357_4_327_0
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%A Laurence Barker
%A Hatice Mutlu
%T A new canonical induction formula for p-permutation modules
%J Comptes Rendus. Mathématique
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Laurence Barker; Hatice Mutlu. A new canonical induction formula for p-permutation modules. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 327-332. doi : 10.1016/j.crma.2019.04.004.

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[3] R. Boltje Linear source modules and trivial source modules, Proc. Symp. Pure Math., Volume 63 (1998), pp. 7-30

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[5] R. Boltje; G. Raggi-Cárdenas; L. Valero-Elizondo The + and + constructions for biset functors, J. Algebra, Volume 523 (2019), pp. 241-273

[6] S. Bouc; J. Thévenaz The primitive idempotents of the p-permutation ring, J. Algebra, Volume 323 (2010), pp. 2905-2915

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