Gildenhuys, Dion; Ribes, Luis Profinite groups and Boolean graphs. (English) Zbl 0428.20018 J. Pure Appl. Algebra 12, 21-47 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 26 Documents MSC: 20E18 Limits, profinite groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20J05 Homological methods in group theory 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 55N30 Sheaf cohomology in algebraic topology 54D30 Compactness Keywords:groups acting on trees; profinite groups; Boolean graphs; oriented graphs; standard graph; pro-C-group; pointed boolean spaces; amalgamated products; colimits; tree product; cohomology groups; groups of global sections of a sheaf; Mayer-Vietoris sequence; one-relator pro-p-groups; HNN pro-p-groups; covering graph PDFBibTeX XMLCite \textit{D. Gildenhuys} and \textit{L. Ribes}, J. Pure Appl. Algebra 12, 21--47 (1978; Zbl 0428.20018) Full Text: DOI References: [1] Binz, E.; Neukirch, J.; Wentzel, G. H., A subgroup theorem for free products of profinite groups, J. Algebra, 19, 104-109 (1971) · Zbl 0232.20052 [2] Brumer, A., Pseudo-compact Algebras, Profinite groups and class formation, J. Algebra, 4, 442-470 (1966) · Zbl 0146.04702 [3] Gildenhuys, D., Pro-\(p\)-groups with one defining relator, Inventiones Math., 5, 357-366 (1968) · Zbl 0159.30601 [4] Gildenhuys, D., Amalgamations of pro-\(p\)-groups with one defining relator, J. Algebra, 41 (1976), to appear. · Zbl 0356.20036 [5] Gildenhuys, D., One-relator groups that are residually of prime power order, J. Austral. Math. Soc., 19, Series A, 385-409 (1975) · Zbl 0325.20034 [6] Gildenhuys, D., The cohomology of groups acting on trees, J. Pure and Applied Algebra, 6, 265-274 (1975) · Zbl 0357.20029 [7] Gildenhuys, D., A generalization of Lyndon’s theorem on the cohomology of one-relator groups, Can. J. Math., 3, 28, 473-480 (1976) · Zbl 0373.20037 [8] Gildenhuys, D.; Lim, C-K, Free Pro-\(C\)-groups, Math. Z., 125, 233-254 (1972) · Zbl 0221.20048 [9] Gildenhuys, D.; Nackay, E., Triple cohomology and Galois cohomology for profinite groups, Comm. in Alg., 1, 6, 459-473 (1974) · Zbl 0289.18008 [10] Gildenhuys, D.; Ribes, L., A Kurosh subgroup theorem for free pro-\(C\)-products of pro-\(C\)-groups, Trans. AMS, 186, 309-329 (1973) · Zbl 0282.20027 [11] Gildenhuys, D.; Ribes, L., On the cohomology of certain topological colimits of pro-\(C\)-groups, J. Alg., 29, 172-197 (1974) · Zbl 0303.20030 [12] Labute, J., Algèbres de Lie et pro-\(p\)-groupes définis par une seule relation, Invent. Math., 4, 142-158 (1967) · Zbl 0212.36303 [13] Neukirch, J., Freie Produkte pro-endlicher Gruppen und ihre Kohomologie, Arch. Math., 22, 337-357 (1971) · Zbl 0254.20023 [14] Ribes, L., On amalgamated products of profinite groups, Math. Z., 123, 357-364 (1971) · Zbl 0218.20031 [15] Ribes, L., Introduction to profinite groups and Galois cohomology, (Queen’s papers in Pure and Applied Maths. (1970), Queen’s University: Queen’s University Kingston, Ont., Canada), no. 24 · Zbl 0948.11043 [16] Ribes, L., Cohomological characterization of amalgamated products of groups, J. Pure and Appl. Algebra, 4, 309-317 (1974) · Zbl 0288.20067 [17] Serre, P., Cohomologie Galoisienne, (Lecture Notes in Mathematics no. 5 (1965), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0812.12002 [18] Serre, P., Groupes discrets, (Lecture Notes (1968-1969), Collège de France: Collège de France Paris) · Zbl 0174.31301 [19] Swan, R., The theory of sheaves (1964), The University of Chicago Press: The University of Chicago Press Chicago · Zbl 0119.25801 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.