We create a method which allows an arbitrary group G with an infrainvariant system ℒ(G) of subgroups to be embedded in a group G* with an infrainvariant system ℒ(G*) of subgroups, so that G *α ∩G ∈ ℒ(G) for every subgroup G *α ∩G ∈ ℒ(G*) and each factor B/A of a jump of subgroups in ℒ(G*) is isomorphic to a factor of a jump in ℒ(G), or to any specified group H. Using this method, we state new results on right-ordered groups. In particular, it is proved that every Conrad right-ordered group is embedded with preservation of order in a Conrad right-ordered group of Hahn type (i.e., a right-ordered group whose factors of jumps of convex subgroups are order isomorphic to the additive group ℝ); every right-ordered Smirnov group is embedded in a right-ordered Smirnov group of Hahn type; a new proof is given for the Holland–McCleary theorem on embedding every linearly ordered group in a linearly ordered group of Hahn type.
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Translated from Algebra i Logika, Vol. 48, No. 5, pp. 606-627, September-October, 2009.
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Kopytov, V.M. Contractions of infrainvariant systems of subgroups. Algebra Logic 48, 344–356 (2009). https://doi.org/10.1007/s10469-009-9066-9
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DOI: https://doi.org/10.1007/s10469-009-9066-9