Abstract
We find necessary and sufficient conditions for the factor groups of the derived series of a pro-p-group with a single defining relation to be torsion free. For such groupsG we prove that the group algebra ℤ pG is a domain and the cohomological dimension ofG is at most 2.
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References
D. Gildenhuys,On pro-p-groups with a single defining relator, Invent. Math.5 (1968), 357–366.
N. Romanovskii,A generalized Freiheitssatz for pro-p-groups, Sib. Math. Zh.27 (1986), 154–170.
J. Labute,Algèbres de Lie et pro-p-groupes définis par une seule relation, Invent. Math.4 (1967), 142–158.
M. Lazard,Sur les groupes nilpotents et les anneaux de Lie, Annales Ecole Normale Supérieure71 (1954), 101–190.
V. Remeslennikov,Embedding theorems for profinite groups, Izv. Akad. Nauk SSSR, Ser. Mat.43 (1979), 399–417.
N. Romanovskii,On some algorithmic problems for soluble groups, Algebra i Logika13 (1974), 26–34.
A. Brumer,Pseudocompact algebras, profinite groups and class formations, J. Algebra4 (1966), 442–470.
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Romanovskii, N.S. On pro-p-groups with a single defining relator. Israel J. Math. 78, 65–73 (1992). https://doi.org/10.1007/BF02801571
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DOI: https://doi.org/10.1007/BF02801571