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Foldings of $$G$$-trees. (English) Zbl 0782.20018
Arboreal group theory, Proc. Workshop, Berkeley/CA (USA) 1988, Publ., Math. Sci. Res. Inst. 19, 355-368 (1991).
Summary: [For the entire collection see Zbl 0744.00026.]
The theory of group actions on trees is used to produce a proof of Grushko’s theorem, which extends to a theorem involving amalgamated free products; this mimics the author’s topological proof, but some new consequences are drawn. Theorems of Shenitzer and Swarup on amalgamations and HNN-extensions over cyclic subgroups are deduced as a consequence and somewhat generalized.

##### MSC:
 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E08 Groups acting on trees 57M05 Fundamental group, presentations, free differential calculus 57M07 Topological methods in group theory