IRREDUCIBLE MODULES AND NORMAL-SUBGROUPS OF PRIME INDEX

Let F be a field, G a finite group, H a normal subgroup of prime index p, and V an irreducible FH-module. If F is algebraically closed and o f characteristic 0, the FG-module induced from V is either irreducible or a direct sum of p pairwise nonisomorphic irreducible modules. It i s shown here that if F is not assumed algebraically closed and its cha racteristic is not 0, then there are not two but six possibilities for the structure of the induced module.