A modular version of Maschke's theorem for groups with cyclic \(p\)-Sylow subgroups
A deformation \(A_ 1\) of an algebra \(A_ 0\) is an algebra which is a specialization of a multiplication structure \(A(t)\) depending on a parameter \(t\) such that \(A(0)\) is isomorphic to \(A_ 0\) and for almost all values \(s\) of \(t\) \(A(s)\) are isomorphic to \(A_ 1\). Let \(k[G]\) be the group algebra of a finite group \(G\) over an algebraically closed field \(k\) of characteristic \(p\) dividing the order of \(G\). The author proves that for every block of a cyclic defect group there exists a semisimple deformation. As a corollary it is obtained the existence of a semisimple deformation of \(k[G]\) if \(G\) has cyclic \(p\)-Sylow subgroups.
scientific article; zbMATH DE number 554139