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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2015 / Cilt: 44 - Sayı: 1

On the structure offinite groupswit hthe given numbersofinvolutions

N. AHANJİDEH
M. Foroudi GHASEMABADI
Sayfa
15–22
Yayın Tarihi
2022-10-18
DOI
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AMSClassification: 20D06,20D20,20E45.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let G beafinitenon-solvablegroup.Inthispaper,weshowthatif1 / 8 ofelementsof G haveordertwo,then G iseitherasimplegroupisomorphicto PSL 2 ( q ) ,where q ∈{ 7 , 8 , 9 } or G ∼= GL2 (4).
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Temel Bulgular & Veri:Z2 .Infactinthispaper,weanswerProblem132in[1].
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Sonuç & Katkı:AMSClassification: 20D06,20D20,20E45.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Let G beafinitenon-solvablegroup.Inthispaper,weshowthatif1 / 8 ofelementsof G haveordertwo,then G iseitherasimplegroupisomorphicto PSL 2 ( q ) ,where q ∈{ 7 , 8 , 9 } or G ∼= GL2 (4). Z2 .Infactinthispaper,weanswerProblem132in[1]. AMSClassification: 20D06,20D20,20E45.

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Bu Makaleye Atıf Yap

AHANJİDEH, N., GHASEMABADI, M. F. (2022). On the structure offinite groupswit hthe given numbersofinvolutions. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 15–22. https://ajindex.com/articles/530265

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Kaynakça (1)

  1. Y.G.BerkovichandE.M.Zhmud, Charactersoffinitegroups,Part2,Amer.Math.Soc. Translationsofmathematicalmonographs,Vol172,1997. [2]R.Brauer,M.SuzukiandG.E.Wall,Acharacterizationoftheone-dimensionaluni-modular projectivegroupsoverfinitefields, IllinoisJ.Math., 2 (1958)718-745. [3]J.H.Conway,R.T.Curtis,S.P.Norton,R.A.ParkerandR.A.Wilson, AtlasofFinite Groups,Clarendon,Oxford,1985. [4]M.DavoudiMonfared,Simplegroupswiththesameinvolutionnumber, EuropeanJournal ofScientificResearch, 66(3) (2011)456-461. [5]O.H.King, Thesubgroupstructureoffiniteclassicalgroupsintermsofgeometricconfigu- rations,Surveyincombinatorics,LondonMath.Soc.LectureNoteSer.327,2005,29-56. [6]TheGapGroups,Gap-Groups,AlgorithmsandProgramming,version4.5, http://www.gapsystem.org,2012. [7]D.Gorenstine, Finitegroups,HarperandRow,NewYork,1968. [8]C.T.C.Wall,Ongroupsconsistingmostlyofinvolutions, Proc.CambridgePhil.Soc., 67 (1970)251-262. [9]J.H.Walter,Thecharacterizationoffinitegroupswithabelian 2-Sylowsubgroups, Annals ofMath./SecondSeries, 89(3) (1969)405-514.