Generation of Iterated Wreath Products Constructed from Almost Simple Groups

TL;DR

This paper investigates the minimal number of generators needed for a sequence of wreath products formed from almost simple groups, providing insights into their algebraic structure and generation properties.

Contribution

It introduces a method to determine the minimum number of generators for iterated wreath products of almost simple groups, a novel approach in group theory.

Findings

Calculated the minimal number of generators for each wreath product in the sequence.

Established bounds and formulas for the generation requirements of these complex groups.

Enhanced understanding of the structure and properties of wreath products from almost simple groups.

Abstract

Let G1, G2, ... be a sequence of almost simple groups and construct a sequence (Wi) of wreath products via W1 = G1 and, for each i > 1, Wi+1 = Gi+1 wr Wi via the regular action of each Gi. We determine the minimum number d(Wi) of generators required for each wreath product in this sequence.