On primitive 2-closed permutation groups of rank at most four

Michael Giudici; Luke Morgan; Jin Xin Zhou

doi:10.48550/arXiv.2110.07896

On primitive 2-closed permutation groups of rank at most four

Michael Giudici, Luke Morgan, Jin Xin Zhou

Mathematics and Statistics

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

Abstract

We characterise the primitive 2-closed groups G of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or G⩽AΓL₁(p^d), the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.

Original language	English
Pages (from-to)	176-205
Number of pages	30
Journal	Journal of Combinatorial Theory. Series B
Volume	158
DOIs	https://doi.org/10.48550/arXiv.2110.07896 https://doi.org/10.1016/j.jctb.2022.09.006
Publication status	Published - Jan 2023

Access to Document

Cite this

@article{9d18746df6f743979c12fbefc4bd1238,

title = "On primitive 2-closed permutation groups of rank at most four",

abstract = "We characterise the primitive 2-closed groups G of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or G⩽AΓL1(pd), the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.",

keywords = "2-closed, Automorphism group, Primitive",

author = "Michael Giudici and Luke Morgan and Zhou, {Jin Xin}",

year = "2023",

month = jan,

doi = "10.48550/arXiv.2110.07896",

language = "English",

volume = "158",

pages = "176--205",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Academic Press",

}

TY - JOUR

T1 - On primitive 2-closed permutation groups of rank at most four

AU - Giudici, Michael

AU - Morgan, Luke

AU - Zhou, Jin Xin

PY - 2023/1

Y1 - 2023/1

N2 - We characterise the primitive 2-closed groups G of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or G⩽AΓL1(pd), the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.

AB - We characterise the primitive 2-closed groups G of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or G⩽AΓL1(pd), the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.

KW - 2-closed

KW - Automorphism group

KW - Primitive

UR - http://www.scopus.com/inward/record.url?scp=85138994133&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2110.07896

DO - 10.48550/arXiv.2110.07896

M3 - Article

AN - SCOPUS:85138994133

SN - 0095-8956

VL - 158

SP - 176

EP - 205

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

On primitive 2-closed permutation groups of rank at most four

Abstract

Access to Document

Other files and links

Fingerprint

Graph symmetry and simple groups

Cite this

On primitive 2-closed permutation groups of rank at most four

Abstract

Access to Document

Other files and links

Fingerprint

Projects

Graph symmetry and simple groups

Cite this