ON COUNTABLE EXTENSIONS OF PRIMARY ABELIAN GROUPS

被引：0

作者：

Danchev, P. V.

机构：

来源：

ARCHIVUM MATHEMATICUM | 2007年 / 43卷 / 01期

关键词：

countable quotient groups; omega-elongations; p(omega+n)-totally projective groups; p(omega+n)-summable groups;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that if A is an abelian p-group with a pure subgroup G so that A/G is at most countable and G is either p(omega+n)-totally projective or p(omega+n)-summable, then A is either p(omega+n)-totally projective or p(omega+n)-summable as well. Moreover, if in addition G is nice in A, then G being either strongly p(omega+n)-totally projective or strongly p(omega+n)-summable implies that so is A. This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective p-groups as well as continues our recent investigations in (Arch. Math. (Brno), 2005 and 2006). Some other related results are also established.

引用

页码：61 / 66

页数：6

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