Groups with a nilpotent-by-finite triple factorization
In many papers on factorized groups one has to study groups \(G=HK=HA=KA\) which have a triple factorization as a product of two subgroups H and K and a normal subgroup A of G. Therefore it is of particular interest to know whether G satisfies some nilpotency requirement whenenver the three subgroups H, K and A satisfy this same nilpotency requirement. A positive answer to this problem is given for the classes of finite-by-nilpotent and nilpotent-by-finite groups provided that G satisfies certain finiteness conditions. The proofs of this paper make use of cohomology theory.
scientific article; zbMATH DE number 4023559