Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups

Abstract

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \dots \wr S_{n_m}$, $n,m\in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special classes of normal subgroups are investigated and their generators are found and presented in the form of Kaloujnine tables. Inverse limit of wreath product of permutation groups is found. Conditions when set-wise stabilizer is normal subgroup are found. In the proposed work a topology of the wreath product as profinite group is studied, is homeomorphic to Cantor set is established.

arXiv comment05 Conferences. I have make a talk by this topic at conference dedicated to A. I. Starostin in Ekaterinburg (2021) 05 October 2021 - 09 October 2021. pp. 108-110. 2) Conference Malcev Meetings Novosibirsk (2025) "Subwreath Product as Structure of Normal Subgroups of Permutational Wreath Products" 3) AGMA May 26, 2026 Normal Subgroups of Iterated Wreath Products of Symmetric Groups

References in corpus (2)

• Generator Sets for the Alternating Group
• Minimal generating systems and properties of Sylow 2-subgroups of alternating group