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A geometrical interpretation of infinite wreath powers. (English) Zbl 1326.20032
Summary: A geometrical construction based on an infinite tree graph is suggested to illustrate the concept of infinite wreath powers of P. Hall. We use techniques based on infinite wreath powers and on this geometrical construction to build a 2-generator group which is not soluble, but in which the normal closure of one of the generators is locally soluble.

20E22 Extensions, wreath products, and other compositions of groups
20F19 Generalizations of solvable and nilpotent groups
20F05 Generators, relations, and presentations of groups
20E08 Groups acting on trees