JournalsjemsVol. 15, No. 6pp. 2061–2079

Modular representations of finite groups with trivial restriction to Sylow subgroups

  • Paul Balmer

    UCLA, Los Angeles, USA
Modular representations of finite groups with trivial restriction to Sylow subgroups cover
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Abstract

Let kk be a field of characteristic pp. Let GG be a finite group of order divisible by pp and PP a pp-Sylow subgroup of GG. We describe the kernel of the restriction homomorphism T(G)T(P)T(G)\to T(P), for T()T(-) the group of endotrivial representations. Our description involves functions Gk×G\to k^\times that we call weak PP-homomorphisms. These are generalizations to possibly non-normal PGP\leq G of the classical homomorphisms G/Pk×G/P\to k^\times appearing in the normal case.

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Paul Balmer, Modular representations of finite groups with trivial restriction to Sylow subgroups. J. Eur. Math. Soc. 15 (2013), no. 6, pp. 2061–2079

DOI 10.4171/JEMS/414