Geodesic
On existence of the universal rational structures for groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 52-63

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It is proved that every group containing the free abelian subgroup of rank $2$ does not admit an universal rational structure. The negative answer to the question by Gersten and Short on the existence for the free abelian of rank $2$ group of such rational structure $L$ for which every subgroup is $L$-rational is derived. 
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     author = {O. V. Grigorenko and V. A. Roman'kov},
     title = {On existence of the universal rational structures for groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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O. V. Grigorenko; V. A. Roman'kov. On existence of the universal rational structures for groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 52-63. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a3/