Tight subgroups in almost completely decomposable groups

A completely decomposable group is a direct sum of groups isomorphic to subgroups of the additive group of rational numbers. An almost completely decomposable group X is a finite essential (abelian) extension of a completely decomposable group A of finite rank. In 1974, Lady [Lad74] initiated a systematic theory of such groups based on the fundamental concept of regulating subgroup. The regulating subgroups can be defined as the completely decomposable subgroups of least index in an almost completely decomposable group. Details on the subsequent developments can be found in the survey article [Mad95] or in the monograph [Mad99].