Construction of the Above and Below Subgroups and Saturated Subgroups of l-groups

Abstract:

      In this paper, an open question on maximal above and below pairs is answered nega-tively and an example is given to show the incorrectness of the proof for Proposition 2.1 in [2]. Furthermore, the construction of saturated subgroup is discussed. The forms of the saturated subgroup generated by a disjoint subset in an l-group and the saturated subgroup generated by any subset in a projectable l-group are determined.