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

Jiaping Lu; Martyn Quick

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

^*Corresponding author for this work

Research output: Working paper › Preprint

Abstract

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

Original language	English
Publisher	arXiv
Number of pages	15
Publication status	Published - 29 Jan 2025

Keywords

Generating sets
Wreath products
Finite groups
Alternating groups
Symmetric groups
Cyclic groups

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https://arxiv.org/abs/2501.17524v1Licence: CC BY

1 Article

Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups
Lu, J. & Quick, M., Aug 2025, In: International Journal of Algebra and Computation. 35, 5, p. 713-731
Research output: Contribution to journal › Article › peer-review

Cite this

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

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

keywords = "Generating sets, Wreath products, Finite groups, Alternating groups, Symmetric groups, Cyclic groups",

author = "Jiaping Lu and Martyn Quick",

note = "Funding: The first author is funded by the China Scholarship Council.",

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T1 - Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups

AU - Lu, Jiaping

AU - Quick, Martyn

N1 - Funding: The first author is funded by the China Scholarship Council.

PY - 2025/1/29

Y1 - 2025/1/29

N2 - Let G1, G2, … be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group. Let us construct a sequence (Wi) of wreath products via W1 = G1 and, for each i ≥ 1, Wi+1 = Gi+1 wr Wi via the natural permutation action. We determine the minimum number d(Wi) of generators required for each wreath product in this sequence.

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

KW - Generating sets

KW - Wreath products

KW - Finite groups

KW - Alternating groups

KW - Symmetric groups

KW - Cyclic groups

M3 - Preprint

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

PB - arXiv

ER -

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

Abstract

Keywords

Access to Document

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Research output

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

Cite this