Modular representations of finite groups with trivial restriction to Sylow subgroups | Zendy

Paul Balmer | Zendy

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Modular representations of finite groups with trivial restriction to Sylow subgroups

Author(s) -

Paul Balmer

Publication year - 2013

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/414

Subject(s) - sylow theorems , mathematics , modular design , locally finite group , pure mathematics , algebra over a field , finite group , combinatorics , group (periodic table) , abelian group , programming language , computer science , chemistry , organic chemistry

Let k be a field of characteristic p. LetG be a finite group of order divisible by p and P a p-Sylow subgroup ofG. We describe the kernel of the restriction homomorphism T (G)→ T (P ), for T (−) the group of endotrivial representations. Our description involves functionsG→ k that we call weak P -homomorphisms. These are generalizations to possibly non-normal P ≤ G of the classical homomorphisms G/P → k appearing in the normal case.

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