COMPLETIONS AND CATEGORICAL COMPACTNESS FOR NILPOTENT GROUPS
作者:
TempleH. Fay,
GaryL. Walls,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1994)
卷期:
Volume 17,
issue 4
页码: 437-451
ISSN:1607-3606
年代: 1994
DOI:10.1080/16073606.1994.9631776
出版商: Taylor & Francis Group
关键词: 20F19;20J15;18A20;torsion-free;nilpotent;radicable;p-cotorsion;p-redud;p-adically complete;categorically compact
数据来源: Taylor
摘要:
We consider reflection functors in the category of nilpotent groups satisfying certain exactness properties for which the Mal'cev completion functor and thep-cotorsion completion functors are prototypical examples. Each of these functors defines a generalized torsion theory, which in turn defines a closure operator on subgroups. This gives rise to the notion of a categorically compact group with respect to the closure operator which we characterize. This approach provides a unified treatment for the categorically compact groups with respect to the Mal'cev completion and with respect to thep-cotorsion completion, the latter being new. We also consider thep-pro-finite completion, suitably restricted to obtain a reflection functor, and characterize the compact groups so arising.
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