�ber aufl�sbare Produkte nilpotenter Gruppen

On Normal Subgroups of Products of Nilpotent Groups

“…This was extended by Kegel in [11] to the case that A and B are finite nilpotent groups (and G is soluble). More generally the first author proved in [1] that the same conclusion holds for soluble products G = AB of two nilpotent subgroups A and B with A =£ B, provided that one of them satisfies the maximum or minimum condition on subgroups. In fact a similar argument applies if one of the two factors A and B is minimax (see [5]).…”

“…THEOREM C. Let G = A 1 Theorem C becomes false if more than one factor is merely locally nilpotent (see Remark 4.1(b)). Some further similar statements for locally finite groups and hyper-(abelian-or-finite) groups with finite torsion-free rank that are products of nilpotent groups are contained in Section 5.…”