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On a problem raised by Alperin and Bass. (English) Zbl 0808.20030
Arboreal group theory, Proc. Workshop, Berkeley/CA (USA) 1988, Publ., Math. Sci. Res. Inst. 19, 35-68 (1991).
Summary: [For the entire collection see Zbl 0744.00026.]
In their paper [Ann. Math. Stud. 111, 265-378 (1987; Zbl 0647.20016)], R. Alperin and H. Bass raised the following: Fundamental problem: Find the group theoretic information carried by a $$\Lambda$$-tree action, analogous to that presented in (J.-P. Serre’s book) “Trees” (1977; Zbl 0369.20013)] for the case $$\Lambda = \mathbb{Z}$$. The aim of this paper is to give a possible answer to the question above by extending to arbitrary ordered abelian groups $$\Lambda$$ the main constructions and results contained in the first chapter of Serre’s book.

##### MSC:
 20E08 Groups acting on trees 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C05 Trees 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) 20J05 Homological methods in group theory
##### Keywords:
$$\Lambda$$-tree action; ordered abelian groups