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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
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Abstract

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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

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