The semiprimitivity problem for group algebras of locally finite groups (Q677426)

This is a step in solving the problem of characterizing locally finite groups \(G\) such that for a given field \(K\) of characteristic \(p>0\) the Jacobson radical of the group algebra \(KG\) is trivial. In this paper the author shows that this is the case if \(G\) has no locally subnormal finite subgroup (i.e. no finite subgroup that is subnormal in every larger finite subgroup of \(G\)). In a subsequent paper [Proc. Lond. Math. Soc., III. Ser. 73, No. 2, 323-357 (1996; Zbl 0863.20004)] the author provides a final solution by showing that the Jacobson radical of \(KG\) is zero if and only if \(G\) has no locally subnormal finite subgroup of order divisible by \(p\).