Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups

2025/01/29 by Jiaping Lu, Martyn Quick, Lu, Jiaping +1 · 1 citation
Engineering · Materials Science · #20E22 20F05 20D06 20B05 #Advanced Materials and Mechanics #FOS: Mathematics #Group Theory (math.GR) #Modular Robots and Swarm Intelligence #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2501.17524

openalex publication_date 2025/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G₁, G₂, ... be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group and construct a sequence (W_i) of wreath products via W₁ = G₁ and, for each i ≥ 1, W_i+1 = G_i+1 wr G_i via the natural permutation action. We determine the minimum number d(W_i) of generators required for each wreath product in this sequence.

Cited by

• Generation of Iterated Wreath Products Constructed from Almost Simple Groups

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