Geodesic
A geometrical interpretation of infinite wreath powers
Algebra and discrete mathematics, Tome 18 (2014) no. 2, pp. 250-267.

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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 constriction to build a 2-generator group which is not soluble, but in which the normal closure of one of the generators is locally soluble.
Keywords: 2-generator groups, soluble groups, locally soluble groups, wreath products, infinite wreath products, graphs, automorphisms of graphs. 
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Vahagn H. Mikaelian. A geometrical interpretation of infinite wreath powers. Algebra and discrete mathematics, Tome 18 (2014) no. 2, pp. 250-267. http://geodesic.mathdoc.fr/item/ADM_2014_18_2_a6/

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