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Ideal series of semigroups play an important role in the examination ofsemigroups which have proper two-sided ideals. But the corresponding theoremscannot be used when left simple (or right simple or simple) semigroups areconsidered. So it is a natural idea that we try to use the group theoreticalmethods (instead of the ring theoretical ones) for the examination of thesesemigroups. The purpose of this paper is to find a suitable type ofsubsemigroups of left simple semigroups which makes possible for us togeneralize some notions (the notion of the normal series and the compositionseries of groups) and some results concerning the groups to the left simplesemigroups. We note that the subsemigroups we are looking for are the reflexiveunitary subsemigroups of left simple semigroups.

Reflexive Unitary Subsemigroups of Left Simple Semigroups