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: $(*)$ 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.\^^MAlgebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.
Keywords: totally projective group, almost totally projective group, countable group, extension
Classification (MSC 2000): 20K10, 20K25, 20K27, 20K40
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