Valuated groups are a topic of central interest in Abelian group theory. On one hand, they provide a viewpoint for classical Abelian theory problems, and on the other hand are of interest in their own right. In this latter regard, there has been some progress in getting structure theorems for certain valuated groups. Complete sets of invariants have been provided for finite direct sums of cyclic valuated p-groups [HRW1], for finite simply presented valuated p-groups (AHW), and for direct sums of torsion-free cyclic valuated groups [AHW]. A general discussion of simply presented valuated p-groups, with an aim toward a structure theory, is presented in [HW]. In [BHW], a basis for a general study of finite valuated p-groups is suggested. However, structure theories for simply presented valuated p-groups and for finite valuated p-groups are only in the initial stages.
Abelian Group Cyclic Group Bounded Group Pure Subgroup Valuate Group
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