A subgroup of ap-group is valuated in a natural way, and every valuatedp-group can be embedded as a valuated subgroup of ap-group. We generalize this theorem to subgroups ofp-valuated groups with values in an arbitrary value domainD. The induced valuation on the subgroup assigns to each element an equivalence class ofD-valuated rooted trees. In the classical caseDis trivial and the equivalence class of trees can be identified with an extended ordinal. The embedding is functorial if some set-theoretic problems can be overcome, which they can be ifDis trivial or equal to the ordinals.
展开▼
