Transitive Simple Subgroups of Wreath Products in Product Action

R.W. Baddeley; Cheryl Praeger; Csaba Schneider

doi:10.1017/S1446788700010156

Transitive Simple Subgroups of Wreath Products in Product Action

R.W. Baddeley
, Cheryl Praeger
, Csaba Schneider

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

14 Citations (Scopus)

Abstract

A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of 'Cartesian decompositions' of the permuted set, relating them to certain 'Cartesian systems of subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.

Original language	English
Pages (from-to)	55-72
Journal	Journal of the Australian Mathematical Society
Volume	77
Issue number	1
DOIs	https://doi.org/10.1017/S1446788700010156
Publication status	Published - 2004

Access to Document

10.1017/S1446788700010156

Cite this

@article{da840030cbdd4bf9af9bd65e7ff154a9,

title = "Transitive Simple Subgroups of Wreath Products in Product Action",

abstract = "A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of 'Cartesian decompositions' of the permuted set, relating them to certain 'Cartesian systems of subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.",

author = "R.W. Baddeley and Cheryl Praeger and Csaba Schneider",

year = "2004",

doi = "10.1017/S1446788700010156",

language = "English",

volume = "77",

pages = "55--72",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Transitive Simple Subgroups of Wreath Products in Product Action

AU - Baddeley, R.W.

AU - Praeger, Cheryl

AU - Schneider, Csaba

PY - 2004

Y1 - 2004

N2 - A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of 'Cartesian decompositions' of the permuted set, relating them to certain 'Cartesian systems of subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.

AB - A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of 'Cartesian decompositions' of the permuted set, relating them to certain 'Cartesian systems of subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.

U2 - 10.1017/S1446788700010156

DO - 10.1017/S1446788700010156

M3 - Article

SN - 1446-7887

VL - 77

SP - 55

EP - 72

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 1

ER -

Transitive Simple Subgroups of Wreath Products in Product Action

Abstract

Access to Document

Fingerprint

Cite this