Finite permutation resolutions
نویسندگان
چکیده
We prove that every finite-dimensional representation of a finite group over field characteristic p admits resolution by p-permutation modules. The proof involves reformulation in terms derived categories.
منابع مشابه
Permutation resolutions for Specht modules
For every composition λ of a positive integer r , we construct a finite chain complex whose terms are direct sums of permutation modules M for the symmetric group Sr with Young subgroup stabilizers Sμ. The construction is combinatorial and can be carried out over every commutative base ring k. We conjecture that for every partition λ the chain complex has homology concentrated in one degree (at...
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1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2023
ISSN: ['1547-7398', '0012-7094']
DOI: https://doi.org/10.1215/00127094-2022-0041