Contractions of infrainvariant systems of subgroups

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.