2015/06/21 by Matteo Vannacci
Mathematics · #math.GR #msc:20B05 #msc:20E18 #msc:20E22 #msc:20F05
published as Arch. Math. (Basel) 105 (2015), no. 3, 205-214 · 9 pages. Updated version with some added references. arXiv admin note: substantial text overlap with arXiv:1412.7809
arxiv created 2015/06/21 · arxiv updated 2016/03/18
Let S be a sequence of finite perfect transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated wreath product in product action of the groups in S is topologically finitely generated, provided that the actions of the groups in S are not regular. We prove that our bound has the right asymptotic behaviour. We also deduce that other infinitely iterated mixed wreath products of groups in S are finitely generated. Finally we apply our methods to find explicitly two generators of infinitely iterated wreath products in product action of special sequences S.