SEMIPRIMITIVITY OF GROUP-ALGEBRAS OF LOCALLY FINITE-GROUPS .2.

Let K be a field of characteristic p > 0, let G be a locally finite gr oup, and let K[G] denote the group algebra of G over K. In this paper we study the Jacobson radical JK[G] when G has a finite subnormal seri es with factors which are either p'-groups, infinite simple, or genera ted by locally subnormal subgroups. For example, we show that if such a group G has no finite locally subnormal subgroup of order divisible by p, then JK[G] = 0. The argument here is a mixture of group ring and group theoretic techniques and requires that we deal more generally w ith twisted group algebras. Furthermore, the proof ultimately depends upon certain consequences of the classification of the finite simple g roups. In particular, we use J.I. Hall's classification of the locally finite finitary simple groups.