Geodesic
On extensions of primary almost totally projective abelian groups
Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 149-155

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Suppose $G$ is a subgroup of the reduced abelian $p$-group $A$. The following two dual results are proved: $(*)$ If $A/G$ is countable and $G$ is an almost totally projective group, then $A$ is an almost totally projective group. $(**)$ If $G$ is countable and nice in $A$ such that $A/G$ is an almost totally projective group, then $A$ is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.
Suppose $G$ is a subgroup of the reduced abelian $p$-group $A$. The following two dual results are proved: $(*)$ If $A/G$ is countable and $G$ is an almost totally projective group, then $A$ is an almost totally projective group. $(**)$ If $G$ is countable and nice in $A$ such that $A/G$ is an almost totally projective group, then $A$ is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.
DOI : 10.21136/MB.2008.134056
Classification : 20K10, 20K25, 20K27, 20K35, 20K40
Keywords: totally projective group; almost totally projective group; countable group; extension 
Danchev, Peter V. On extensions of primary almost totally projective abelian groups. Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 149-155. doi: 10.21136/MB.2008.134056
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