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

D. Gildenhuys, S. Ivanov, O. Kharlampovich

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1199-1207
Number of pages9
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number6
StatePublished - 1994
Externally publishedYes


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