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\(SD\)-groups and embeddings. (English) Zbl 1281.20036
Summary: We show that every countable \(SD\)-group \(G\) can be subnormally embedded into a two-generator \(SD\)-group \(H\). This embedding can have additional properties: if the group \(G\) is fully ordered then the group \(H\) can be chosen to also be fully ordered. For any non-trivial word set \(V\) this embedding can be constructed so that the image of \(G\) under the embedding lies in the verbal subgroup \(V(H)\) of \(H\).

MSC:
20F14 Derived series, central series, and generalizations for groups
20F19 Generalizations of solvable and nilpotent groups
20E10 Quasivarieties and varieties of groups
20E15 Chains and lattices of subgroups, subnormal subgroups
20F60 Ordered groups (group-theoretic aspects)
20E07 Subgroup theorems; subgroup growth
20F05 Generators, relations, and presentations of groups
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