Zalesskij, P. A.; Mel’nikov, O. V. Fundamental groups of graphs of profinite groups. (English. Russian original) Zbl 0726.20015 Leningr. Math. J. 1, No. 4, 921-940 (1990); translation from Algebra Anal. 1, No. 4, 117-135 (1989). The paper completes the construction of a profinite analog of the Bass-Serre theory of group actions on trees. The notion of a fundamental group for any graph of profinite groups is introduced and a characterization in terms of the canonical profinite graph is given (theorems 3.4, 4.1). The results are extended in §5 to varieties of pro-C-groups and applied to a description of finite, nilpotent and other subgroups of the fundamental group. Reviewer: Yu.N.Mukhin (Sverdlovsk) Cited in 2 ReviewsCited in 11 Documents MSC: 20E18 Limits, profinite groups 20E08 Groups acting on trees 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E07 Subgroup theorems; subgroup growth 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:Bass-Serre theory; group actions on trees; fundamental groups; graphs of profinite groups; profinite graphs; varieties of pro-C-groups; subgroups PDFBibTeX XMLCite \textit{P. A. Zalesskij} and \textit{O. V. Mel'nikov}, Leningr. Math. J. 1, No. 4, 921--940 (1990; Zbl 0726.20015); translation from Algebra Anal. 1, No. 4, 117--135 (1989)