Generation of Generalised Wreath Products of Symmetric Groups

TL;DR

This paper introduces a construction called the generalized wreath product of symmetric groups based on a finite poset and determines the minimal number of generators needed for such a product.

Contribution

It defines the generalized wreath product for symmetric groups indexed by a poset and calculates the minimal generating set size for these groups.

Findings

Determined the minimal number of generators for the generalized wreath product.

Provided a construction method for generalized wreath products of symmetric groups.

Abstract

Let I be a finite partially ordered set and let (Sym({\Delta}i),{\Delta}i)i be a sequence of symmetric groups indexed by I. Construct the generalised wreath product (F, {\Delta}) on this sequence of permutation groups. We determine the minimum number d(F) of generators required for this generalised wreath product.