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MATHEMATICA BOHEMICA, Vol. 133, No. 2, pp. 149-155 (2008)
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On extensions of primary almost totally projective abelian groups

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Peter V. Danchev

* Peter V. Danchev*, 13, General Kutuzov Street, bl. 7, floor 2, apart. 4, 4003 Plovdiv, Bulgaria, e-mail: ` pvdanchev@yahoo.com`

**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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