On extensions of primary almost totally projective abelian groups

Danchev, Peter Vassilev. "On extensions of primary almost totally projective abelian groups." Mathematica Bohemica 133.2 (2008): 149-155. <http://eudml.org/doc/250523>.

@article{Danchev2008,
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. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.},
author = {Danchev, Peter Vassilev},
journal = {Mathematica Bohemica},
keywords = {totally projective group; almost totally projective group; countable group; extension; almost totally projective groups; countable Abelian -groups; extensions},
language = {eng},
number = {2},
pages = {149-155},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On extensions of primary almost totally projective abelian groups},
url = {http://eudml.org/doc/250523},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Danchev, Peter Vassilev
TI - On extensions of primary almost totally projective abelian groups
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 2
SP - 149
EP - 155
AB - 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.
LA - eng
KW - totally projective group; almost totally projective group; countable group; extension; almost totally projective groups; countable Abelian -groups; extensions
UR - http://eudml.org/doc/250523
ER -