Graph-wreath products and finiteness conditions
Abstract
A notion of graph-wreath product is introduced. We obtain sufficient conditions for these products to satisfy the topologically inspired finiteness condition type Fn. Under various additional assumptions we show that these conditions are necessary. Our results generalise results of Cornulier about wreath products in case n=2. Graph-wreath products include classical permutational wreath products and semidirect products of right-angled Artin groups by groups of automorphisms amongst others.
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