Abstract:
A finite dinilpotent grouup G is one that can be written as the
product of two finite nilpotent groups, A and B say. A finite
dinilpotent group is always soluble. If A is abelian and B is
metabelian we show that a bound on the derived length given by
Kazarin can be improved. We show that G has derived length at
most 3 unless G contains a section with a well defined structure;
in particular if G is of odd order, G has derived length at
most 3.