On the normalizer of an iterated wreath product

2023/02/23 by Fernando Szechtman, Szechtman, Fernando
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2302.12040

openalex publication_date 2023/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a group G and n≥ 0, let W(G,n) be the associated iterated wreath product -- unrestricted when G is infinite -- viewed as a permutation group on Gⁿ. We prove that the normalizer of W(G,n) in the symmetric group S(Gⁿ) is equal to M_n\ltimes W(G,n), where M_n is isomorphic to~Aut(G)ⁿ. The action of Aut(G)ⁿ on W(G,n) is recursively described.

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