  We study groups, all maximal nilpotent subgroups of class at most $k$ in
which are malnormal. We show that such groups share many similar properties
with the ordinary CSA groups. Similarly, we introduce the class of {\em
nilpotency transitive} groups and we show that in presence of a special
residuality condition, these two concepts are the equivalent. As a result, we
see that the theory of CSA and CT groups is a small part of a more general
idea.
