Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-17T16:09:25.721Z Has data issue: false hasContentIssue false
  • English
  • Français

On a family of one-relator pro-p-groups

Published online by Cambridge University Press:  14 November 2011

D. Gildenhuys ,
S. Ivanov  and
O. Kharlampovich
D. Gildenhuys
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, CanadaH3A 2K6
S. Ivanov
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, CanadaH3A 2K6
O. Kharlampovich
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, CanadaH3A 2K6
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of describing one-relator pro-p-groups of cohomological dimension two (along the lines of Lyndon's description of discrete one-relator groups of cohomological dimension two) is still open. The known method of passing by means of a suitable p-filtration to a graded Lie algebra is not applicable to the family of one-relator pro-p-groups presented in this article, since the relators cannot be separated from the p-th powers in the free pro-p-group. In terms of the p-filtrations, the relators come arbitrarily close to a p-th power, yet the groups they define have cohomological dimension two.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1199 - 1207
Copyright
Copyright © Royal Society of Edinburgh 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Brumer, A.. Pseudocompact algebras, profinite groups and class formations. J. Algebra 4 (1966), 442–470.CrossRefGoogle Scholar
2Gildenhuys, D.. On pro-p-groups with a single denning relator. Invent. Math. 5 (1968), 357–366.CrossRefGoogle Scholar
3Gildenhuys, D.. On the cohomology of certain topological colimits of ℘if-groups. J. Algebra 29 (1974), 172–197.CrossRefGoogle Scholar
4Gildenhuys, D.. Amalgamations of one-relator pro-p-groups. J. Algebra 42 (1976), 11–25.CrossRefGoogle Scholar
5Gildenhuys, D. and Lim, C.-K.. Free pro-℘-groups. Math. Z. 124 (1972), 233–254.CrossRefGoogle Scholar
6Koch, H.. Über pro-p-gruppen der kohomologischen dimension 2. Math. Nachr. 78 (1977), 285–289.CrossRefGoogle Scholar
7Labute, J.. Dumuskin groups of rank R0. Bull. Soc. Math. France 94 (1966), 211–244.CrossRefGoogle Scholar
8Labute, J.. Algebres des lie et pro-p-groupes definis par une seule relation. Invent. Math. 4 (1967), 142–158.CrossRefGoogle Scholar
9Labute, J.. Classification of demuskin groups. Canad. J. Math. 19 (1967), 106–132.CrossRefGoogle Scholar
10Lazard, M.. Groupes analytiques p-adiques. Publ. Inst. Hautes Etudes Sri. 26 (1965), 000–000.Google Scholar
11Lyndon, R.. Cohomology theory of a group with a single defining relation. Ann. Math. 52 (1950), 650–665.CrossRefGoogle Scholar
12Romanovskii, N. S.. On pro-p-groups with a single defining relator (Preprint).Google Scholar
13Serre, J.-P.. Structure de certains pro-p-groups. Seminaire Bourbaki 252 (1962/1963). 000–000.Google Scholar