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

Jiaping Lu; Martyn Quick

doi:10.1142/S0218196725500201

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

Jiaping Lu, Martyn Quick^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	713-731
Journal	International Journal of Algebra and Computation
Volume	35
Issue number	5
Early online date	7 Jun 2025
DOIs	https://doi.org/10.1142/S0218196725500201
Publication status	Published - Aug 2025

Keywords

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

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10.1142/S0218196725500201

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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.",

year = "2025",

month = aug,

doi = "10.1142/S0218196725500201",

language = "English",

volume = "35",

pages = "713--731",

journal = "International Journal of Algebra and Computation",

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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 - 2025/8

Y1 - 2025/8

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

UR - https://www.scopus.com/pages/publications/105007550839

U2 - 10.1142/S0218196725500201

DO - 10.1142/S0218196725500201

M3 - Article

SN - 0218-1967

VL - 35

SP - 713

EP - 731

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 5

ER -

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

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Keywords

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

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