Simplicity condition for the fundamental ideal of the modular group algebra of a locally finite group

A criterion for the simplicity of the fundamental ideal of the group ring of a locally finite group is given. With its help the simplicity of this ideal for the group PSL(2, F), where F is an infinite field that is a union of its finite subfields, is proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1088–1091, July–August, 1991.