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Compact coGalois groups

Published online by Cambridge University Press:  01 March 2000

EDGAR E. ENOCHS ,
J. R. GARCÍA ROZAS ,
LUIS OYONARTE  and
OVERTOUN M. G. JENDA
EDGAR E. ENOCHS
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, U.S.A. e-mail: [email protected]
J. R. GARCÍA ROZAS
Affiliation:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain; e-mail: [email protected], [email protected]
LUIS OYONARTE
Affiliation:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain; e-mail: [email protected], [email protected]
OVERTOUN M. G. JENDA
Affiliation:
Department of Discrete and Statistical Sciences, 120 Mathematical Annex, Auburn University, Auburn, AL 36849-5307, U.S.A. e-mail: [email protected]
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Abstract

In this paper we extend the concept of the group of covering automorphisms associated to a universal covering space ϕ: U → X (where X is a connected topological manifold), to the case of left (or right) minimal approximations. In the case of torsion-free coverings of abelian groups we exhibit a topology on these groups which makes them into topological groups and we give necessary and sufficient conditions for these groups to be compact. Finally we prove that when these groups are compact they are pronilpotent (Theorem 5·3). We also characterize when these groups are torsion-free (Proposition 5·4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 2 , March 2000 , pp. 233 - 244
Copyright
© The Cambridge Philosophical Society 2000

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