A Generalization of Szep’s Conjecture for Almost Simple Groups

Nick Gill; Michael Giudici; Pablo Spiga

doi:10.1007/s10013-023-00635-1

A Generalization of Szep’s Conjecture for Almost Simple Groups

Nick Gill, Michael Giudici, Pablo Spiga

Mathematics and Statistics

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

3 Citations (Web of Science)

Abstract

We prove a natural generalization of Szep’s conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x, y∈ G\ { 1 } with G= N_G(⟨ x⟩) N_G(⟨ y⟩) , where we are denoting by N_G(⟨ x⟩) and by N_G(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩ . As a consequence of this result, we classify all possible group elements x, y∈ G\ { 1 } with G= C_G(x) C_G(y) .

Original language	English
Pages (from-to)	325-359
Number of pages	35
Journal	Vietnam Journal of Mathematics
Volume	52
Issue number	2
Early online date	19 Jul 2023
DOIs	https://doi.org/10.1007/s10013-023-00635-1
Publication status	Published - Apr 2024

Access to Document

10.1007/s10013-023-00635-1Licence: CC BY

Cite this

@article{11c75676e7c644c8aa4eaea4288b5e43,

title = "A Generalization of Szep{\textquoteright}s Conjecture for Almost Simple Groups",

abstract = "We prove a natural generalization of Szep{\textquoteright}s conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x, y∈ G\ { 1 } with G= NG(⟨ x⟩) NG(⟨ y⟩) , where we are denoting by NG(⟨ x⟩) and by NG(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩ . As a consequence of this result, we classify all possible group elements x, y∈ G\ { 1 } with G= CG(x) CG(y) .",

keywords = "Almost simple, Group factorization, Szep{\textquoteright}s conjecture",

author = "Nick Gill and Michael Giudici and Pablo Spiga",

note = "Funding Information: The second author was supported by the Australian Research Council Discovery Project DP160102323. Funding Information: Open access funding provided by Universit{\`a} degli Studi di Milano - Bicocca within the CRUI-CARE Agreement. Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2024",

month = apr,

doi = "10.1007/s10013-023-00635-1",

language = "English",

volume = "52",

pages = "325--359",

journal = "Vietnam Journal of Mathematics",

issn = "2305-221X",

publisher = "Springer Science + Business Media",

number = "2",

}

TY - JOUR

T1 - A Generalization of Szep’s Conjecture for Almost Simple Groups

AU - Gill, Nick

AU - Giudici, Michael

AU - Spiga, Pablo

N1 - Funding Information: The second author was supported by the Australian Research Council Discovery Project DP160102323. Funding Information: Open access funding provided by Università degli Studi di Milano - Bicocca within the CRUI-CARE Agreement. Publisher Copyright: © 2023, The Author(s).

PY - 2024/4

Y1 - 2024/4

N2 - We prove a natural generalization of Szep’s conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x, y∈ G\ { 1 } with G= NG(⟨ x⟩) NG(⟨ y⟩) , where we are denoting by NG(⟨ x⟩) and by NG(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩ . As a consequence of this result, we classify all possible group elements x, y∈ G\ { 1 } with G= CG(x) CG(y) .

AB - We prove a natural generalization of Szep’s conjecture. Given an almost simple group G with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements x, y∈ G\ { 1 } with G= NG(⟨ x⟩) NG(⟨ y⟩) , where we are denoting by NG(⟨ x⟩) and by NG(⟨ y⟩) the normalizers of the cyclic subgroups ⟨ x⟩ and ⟨ y⟩ . As a consequence of this result, we classify all possible group elements x, y∈ G\ { 1 } with G= CG(x) CG(y) .

KW - Almost simple

KW - Group factorization

KW - Szep’s conjecture

UR - http://www.scopus.com/inward/record.url?scp=85165035913&partnerID=8YFLogxK

U2 - 10.1007/s10013-023-00635-1

DO - 10.1007/s10013-023-00635-1

M3 - Article

AN - SCOPUS:85165035913

SN - 2305-221X

VL - 52

SP - 325

EP - 359

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 2

ER -

A Generalization of Szep’s Conjecture for Almost Simple Groups

Abstract

Access to Document

Other files and links

Fingerprint

Permutation groups: factorisations, structure and applications

Cite this

A Generalization of Szep’s Conjecture for Almost Simple Groups

Abstract

Access to Document

Other files and links

Fingerprint

Projects

Permutation groups: factorisations, structure and applications

Cite this