On the first cohomology of a group with coefficients in a simple module
The authors give a proof of the following result. Let k be a field and let N be a subnormal subgroup of the group G. If V is a simple kG-module and if U is a simple kN-module of V on which N acts nontrivially, then one has dim \(H^ 1(G,V)\leq \dim H^ 1(N,U)\). This improves a result of \textit{M. Aschbacher} and \textit{L. Scott} [J. Algebra 92, 44-80 (1985; Zbl 0549.20011)].
scientific article; zbMATH DE number 3953095