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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.

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.)
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