SCHUR RING AND QUASI-SIMPLE MODULES

Abstract

Let R be a ring of algebraic integers of an algebraic number field F and let G ≤ GLn(R) be a finite group. In this paper we show that the R-span of G is just the matrix ring Mn(R) of the n X n-matrices over R if and only if G/Opi(G) is absolutely simple for all pi ∈ π, where π is the set of the positive prime divisors of |G| and Opi(G) is the largest normal pi-subgroup.