  Ideal series of semigroups play an important role in the examination of
semigroups which have proper two-sided ideals. But the corresponding theorems
cannot be used when left simple (or right simple or simple) semigroups are
considered. So it is a natural idea that we try to use the group theoretical
methods (instead of the ring theoretical ones) for the examination of these
semigroups. The purpose of this paper is to find a suitable type of
subsemigroups of left simple semigroups which makes possible for us to
generalize some notions (the notion of the normal series and the composition
series of groups) and some results concerning the groups to the left simple
semigroups. We note that the subsemigroups we are looking for are the reflexive
unitary subsemigroups of left simple semigroups.
