On group stable commutative separable semisimple subalgebras

Abstract.

In a G-algebra A of a p-group G over a perfect ground field there is a commutative separable semisimple G-subalgebra such that any traces on relative projectivity in A can be controlled in the subalgebra; and in a residually central sense, the maximal such subalgebras form exactly one $(A^G)^*$-conjugacy class. Applying to modules, the induced module of an indecomposable module of a subnormal subgroup of p- primary index is characterized.