On group stable commutative separable semisimple subalgebras. (Q1566326)

Green's Indecomposability Theorem is an important tool in representation theory of finite groups. \textit{L. Puig} [Math. Z. 166, 117-129 (1979; Zbl 0387.16006)] has proved a version of this theorem which deals with a \(P\)-algebra \(A\), for a finite \(p\)-group \(P\), and \(P\)-stable commutative subalgebras of \(A\) which are generated by idempotents. Puig's theorem mainly applies to ``large'' ground rings. The paper under review generalizes Puig's result to ``small'' ground rings, replacing the \(P\)-stable commutative subalgebras which are generated by idempotents by \(P\)-stable commutative separable subalgebras.