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LI Wanting; LING Bo

doi:10.13471/j.cnki.acta.snus.2021A003

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A 2-transitive 7-valent non-normal Cayley graph on the alternating group

A_{167}

Research articles | 更新时间：2023-11-01

- A 2-transitive 7-valent non-normal Cayley graph on the alternating group $A_{167}$
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 6, Pages: 166-171(2022)
- 作者机构：
  
  云南民族大学数学与计算机科学学院，云南昆明 650504
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2021A003
  CLC： O157.5
- Published：25 November 2022，
  
  Published Online：28 April 2022，
  
  Received：10 January 2021，
  
  Accepted：08 May 2021
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李婉婷,凌波.交错群A167上的连通7度2-传递非正规Cayley图[J].中山大学学报(自然科学版),2022,61(06):166-171.

LI Wanting,LING Bo.A 2-transitive 7-valent non-normal Cayley graph on the alternating group A167[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(06):166-171.
李婉婷,凌波.交错群A167上的连通7度2-传递非正规Cayley图[J].中山大学学报(自然科学版),2022,61(06):166-171. DOI： 10.13471/j.cnki.acta.snus.2021A003.

LI Wanting,LING Bo.A 2-transitive 7-valent non-normal Cayley graph on the alternating group A167[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(06):166-171. DOI： 10.13471/j.cnki.acta.snus.2021A003.

A 2-transitive 7-valent non-normal Cayley graph on the alternating group

A_{167}

PDF Download

摘要

在交错群

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432090&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432080&type=

4.74133301

3.21733332

上构造了一个具有非可解点稳定子群的连通7度2-传递非正规Cayley图，并证明了其全自同构群同构于

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432120&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432113&type=

4.74133301

3.21733332

。这是目前为止第一个关于有限非交换单群上的具有非可解点稳定子群的连通7度2-传递非正规Cayley图的例子。

Abstract

We construct an example of a non-normal 2-transitive 7-valent Cayley graph on the alternating group

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432159&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432142&type=

5.41866684

3.72533321

， where the vertex stabilizer is insoluable， and show that the full automorphism group of this graph is isomorphic to the alternating group

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432191&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49432171&type=

5.41866684

3.72533321

. So far， this is the first example of connected 2-transitive 7-valent non-normal Cayley graph with insoluable vertex stabilizer on finite non-abelian simple groups.

关键词

对称图单群全自同构群非正规Cayley图

Keywords

symmetric graphsimple groupfull automorphism groupnon-normal Cayley graph

references

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LING B， LOU B G. A 2-arc transitive pentavalent Cayley graph of <math id="M363"><msub><mrow><mi mathvariant="bold">A</mi></mrow><mrow><mn mathvariant="normal">39</mn></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435823&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435805&type=4.233333593.21733332 ［J］. Bull Aust Math Soc， 2016， 93： 441-446.

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PAN J M， YIN F G， LING B. Arc-transitive Cayley graphs on non-abelian simple groups with soluble vertex stabilizers and valency seven ［J］. Discrete Math， 2019， 342（3）： 689-696.

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A 2-transitive pentavalent nonnormal Cayley graph on the alternating group A₁₁₉

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Wan Ting LI

Bo LING

LING Bo

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A 2-transitive 7-valent non-normal Cayley graph on the alternating group A167

DOI：10.13471/j.cnki.acta.snus.2021A003

摘要

Abstract

关键词

Keywords

references

A 2-transitive 7-valent non-normal Cayley graph on the alternating group $A_{167}$