Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T05:57:25.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Local Freeness of Profinite Groups

Published online by Cambridge University Press:  20 November 2018

Andrew Pletch
Andrew Pletch*
Affiliation:
Instttuto de Mathemática, Universidade de Sāo Paulo, Sāo Paulo Brasil
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we discuss the relationship between local properties such as freeness and projectivity of a group and the freeness or projectivity of its pro-C-completion. We show that for certain classes, C, of finite groups (e.g. p-groups, nilpotent groups, super-solvable groups) the pro-C-completion of a locally free pro-C-group is a free pro-C-group. We also show that under certain circumstances the converse is also true but we leave open the question, for example, of whether a locally free pro-p-group is free.

Keywords

20E18
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 441 - 446
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Bourbaki, N., Theory of Sets. Paris: Herman, 1968.Google Scholar
2. Gruenberg, K., Projective profinite Groups. J. London Math. Soc. 42 (1967), pp. 155-165.Google Scholar
3. Magnus, W., A. Karrass and Solitar, D., Combinatorial Group Theory. London-New York: Interscience 1966.Google Scholar
4. Ribes, L., Introduction to Profinitie Groups and Galois Cohomology. Queen's Papers in Pure and Applied Mathematics, No. 24, Kingston, Ontario, 1970.Google Scholar
5. J-Serre, P., Letter to the author dated 26 mars, 1975.Google Scholar