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On embeddings of countable generalized soluble groups into two-generated groups. (English) Zbl 1006.20026
Well-known results of B. H. Neumann, H. Neumann and G. Higman state that a countable group can be embedded into a two-generator group. B. H. Neumann and L. G. Kovács have also shown that this is possible within the class of SI* (SN*)-groups. The author shows that it is also possible to embed the countable group as a subnormal subgroup (also within the classes of SI (SN)-groups). The length of the normal (subnormal) series in the case of SI* (SN*)-groups can be made to increase only by 2, and orders can be preserved.

MSC:
20F19 Generalizations of solvable and nilpotent 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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