On extensions of primary almost totally projective abelian groups

Peter Vassilev Danchev

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 2, page 149-155
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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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 -

References

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  1. Generalized Dieudonné and Honda criteria, Alg. Colloq. 15 (2008). (2008) Zbl1154.20043MR2418776
  2. Generalized Dieudonné and Hill criteria, Portugal. Math. 65 (2008), 121–142. (2008) Zbl1146.20034MR2387091
  3. Generalized Wallace theorems, (to appear). (to appear) MR2498370
  4. Dual Wallace theorems. Submitted, . 
  5. Infinite Abelian Groups, II, Mir, Moskva, 1977. (Russian) (1977) MR0457533
  6. Almost coproducts of finite cyclic groups, Commentat. Math. Univ. Carolin. 36 (1995), 795–804. (1995) Zbl0845.20038MR1378700
  7. Almost totally projective groups, Czech. Math. J. 46 (1996), 249–258. (1996) MR1388614
  8. Isotype separable subgroups of totally projective groups, Proc. Padova Conf. 1994, Abelian Groups and Modules, A. Facchini (ed.), Kluwer Acad. Publ., Dordrecht, 1995, pp. 291–300. (1995) MR1378207
  9. On mixed groups of torsion-free rank one with totally projective primary components, J. Algebra 17 (1971), 482–488. (1971) Zbl0215.39902MR0272891

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