Group extensions by primary abelian groups
نویسندگان
چکیده
منابع مشابه
On component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملOn Countable Extensions of Primary Abelian Groups
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-totally projective or p-summable, then A is either p-totally projective or p-summable as well. Moreover, if in addition G is nice in A, then G being either strongly p-totally projective or strongly p-summable implies that so is A. This generalizes a classical result of Wallace ...
متن کاملOn Extensions of Primary Almost Totally Projective Abelian Groups
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 du...
متن کاملon component extensions locally compact abelian groups
let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...
متن کاملCombinable Extensions of Abelian Groups
The design of decision procedures for combinations of theories sharing some arithmetic fragment is a challenging problem in verification. One possible solution is to apply a combination method à la Nelson-Oppen, like the one developed by Ghilardi for unions of non-disjoint theories. We show how to apply this non-disjoint combination method with the theory of abelian groups as shared theory. We ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1960
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1960-0131449-1