On extensions of primary almost totally projective abelian groups

Abstract: Suppose $G$ is a subgroup of the reduced abelian $p$-group $A$. The following two dual results are proved: \endgraf $(*)$ If $A/G$ is countable and $G$ is an almost totally projective group, then $A$ is an almost totally projective group. \endgraf $(**)$ 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. \endgraf These results somewhat strengthen theorems due to Wallace (J.\^^MAlgebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.

Keywords: totally projective group, almost totally projective group, countable group, extension

Classification (MSC2000): 20K10, 20K25, 20K27, 20K40

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