Compact nilpotent groups
作者:
Temple H. Fay,
Gary L. Walls,
期刊:
Communications in Algebra
(Taylor Available online 1989)
卷期:
Volume 17,
issue 9
页码: 2255-2268
ISSN:0092-7872
年代: 1989
DOI:10.1080/00927878908823846
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
Herrlich, Salicrup, and Strecker [HSS] have shown that Kuratowski’s Theorem, namely, that a space X is compact if and only if for every space Y, the projection π2X×Y → Y is a closed map, can be interpreted categorically, and hence generalized and applied in a wider settin than the category of topological spaces. The first author, in an earlier paperj [Fl] , applied this categorical interpretation of compactness in categories of R-modules, obtaining a theory of compactness for each torsion theory T. In the case of the category of abelian groups and a hereditary torsion theory T, a group G is T-compact provided G/TG is a T-injective. In this note, the notion of compact is extended to the categories of hypercentral groups, nilpotent groups, and of FC-groups; it is shown that ifTπdenotes the π-torsion subgroup functor for a set of primes π, then a group G isTπ-compact provided G/TπG is π-complete, extending the abelian group result in a natural way.
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