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Profinite completions of the fundamental group of the Klein bottle. (English) Zbl 0609.57001

Author’s summary: ”A compactification of the fundamental group of the Klein bottle is obtained by means of the determination of its profinite completion. The Sylow decomposition of this group is expressed in terms of p-profinite completions for each prime number p. Several finiteness, centrality and radical properties are established.”
Reviewer: S.J.Pride

MSC:

57M05 Fundamental group, presentations, free differential calculus
20E18 Limits, profinite groups
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References:

[1] C. Godbillon: Éléments de Topologie Algébrique. Hermann, Paris, 1971. · Zbl 0218.55001
[2] D. J. S. Robinson: Finiteness Conditions and Generalized Soluble Groups, Parts 1 - 2. Ergebnisse der Mathematik und Ihrer Grenzgebiete, Vols. 62-63, Springer-Verlag, Berlin- Heidelberg-New York, 1972.
[3] S. S. Shatz: Profinite Groups, Arithmetic, and Geometry. Annals of Mathematics Studies, No. 67, Princeton Univ. Press, Princeton, N.J., 1972. · Zbl 0236.12002
[4] H. H. Torriani: Subgroups of the Klein bottle group. submitted. · Zbl 0673.57002
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