Geodesic
Modular representations of finite groups with trivial restriction to Sylow subgroups
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2061-2079

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DOI

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)→T(P), for T(−) the group of endotrivial representations. Our description involves functions G→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.
DOI : 10.4171/jems/414
Classification : 20-XX
Keywords: endotrivial module, trivial restriction to Sylow, weak homomorphism 
Paul Balmer. Modular representations of finite groups with trivial restriction to Sylow subgroups. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2061-2079. doi: 10.4171/jems/414
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     author = {Paul Balmer},
     title = {Modular representations of finite groups with trivial restriction to {Sylow} subgroups},
     journal = {Journal of the European Mathematical Society},
     pages = {2061--2079},
     year = {2013},
     volume = {15},
     number = {6},
     doi = {10.4171/jems/414},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/414/}
}
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