Clifford theory for semisimple \(G\)-groups
Let \(G\) be a finite group, \(H\) a subgroup of \(G\), and \(A\) a group acted on by \(H\). \(A\) is said to be an irreducible \(H\)-group if it has no non-trivial proper normal \(H\)-invariant subgroups, and \(A\) is semisimple if it is a direct product of non-Abelian irreducible \(H\)-groups. Starting with this concept, the authors define a based \(G\)-functor, and using the results of the previous paper [J. Algebra 231, No. 2, 601-613 (2000; see the preceding review Zbl 0976.20003)], they prove the existence of a Clifford theory for this \(G\)-functor.
scientific article; zbMATH DE number 1526426