On extensions of primary almost totally projective abelian groups

Danchev, Peter V.

Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 149-155.

Résumé

Suppose $G$ is a subgroup of the reduced abelian $p$-group $A$. The following two dual results are proved: $(\ast )$ If $A/G$ is countable and $G$ is an almost totally projective group, then $A$ is an almost totally projective group. $(\ast \ast )$ 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.

Détail

DOI : 10.21136/MB.2008.134056

Classification : 20K10, 20K25, 20K27, 20K35, 20K40
Mots-clés : totally projective group; almost totally projective group; countable group; extension