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

TL;DR

This paper investigates the structure and properties of normal subgroups in finite and infinite iterated wreath products of symmetric and alternating groups, providing classifications, generators, and inverse limits.

Contribution

It introduces a detailed analysis of normal subgroups in iterated wreath products, including classifications, generators, and the inverse limit structure.

Findings

Normal subgroups are classified and their properties are established.

Generators for special classes of normal subgroups are explicitly constructed.

The inverse limit of wreath products of permutation groups is characterized.

Abstract

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ 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.