Geodesic
Abelian group pairs having a trivial coGalois group
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1069-1081.

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Torsion-free covers are considered for objects in the category $q_2.$ Objects in the category $q_2$ are just maps in $R$-Mod. For $R = {\mathbb Z},$ we find necessary and sufficient conditions for the coGalois group $G(A \longrightarrow B),$ associated to a torsion-free cover, to be trivial for an object $A \longrightarrow B$ in $q_2.$ Our results generalize those of E. Enochs and J. Rado for abelian groups.
Classification : 13C11, 16D10, 16G20, 20K30, 20K40
Keywords: coGalois group; torsion-free covers; pairs of modules 
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     author = {Hill, Paul},
     title = {Abelian group pairs having a trivial {coGalois} group},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1069--1081},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {2008},
     mrnumber = {2471166},
     zbl = {1174.20016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_4_a13/}
}
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Hill, Paul. Abelian group pairs having a trivial coGalois group. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1069-1081. http://geodesic.mathdoc.fr/item/CMJ_2008__58_4_a13/