Characterization of finitely generated infinitely iterated wreath products

Details Characterization of finitely generated infinitely iterated wreath products Characterization of finitely generated infinitely iterated wreath products

2011-04-21

arxiv.org/abs/1104.4198v1

Mathematics

Group Theory

Scientific paper

Given a sequence of $(G_i)_{i \in \N}$ of finite transitive groups of degree $n_i$, let $W_\infty$ be the inverse limit of the iterated permutational wreath products of the first m groups. We prove that $W_\infty$ is (topologically) finitely generated if and only if $\prod_{i=1}^{\infty} (G_i/G_i')$ is finitely generated and the growth of the minimal number of generators of $G_i$ is bounded by $ d...n_1...n_{i-1}$ for a constant $d$. Moreover we give a criterion to decide whether $W_\infty$ is positively finitely generated.

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