FINITE ALMOST SIMPLE GROUPS WHOSE GRUENBERG-KEGEL GRAPHS COINCIDE WITH GRUENBERG-KEGEL GRAPHS OF SOLVABLE GROUPS

被引：6

作者：

Gorshkov, I. B. ^{[1
]}

Maslova, N., V ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Ural Branch, Krasovskii Inst Math & Mech, Ul S Kovalevskoi 16, Ekaterinburg 620990, Russia

[2] Eltsyn Ural Fed Univ, Ul Mira 19, Ekaterinburg 620002, Russia

来源：

ALGEBRA AND LOGIC | 2018年 / 57卷 / 02期

基金：

巴西圣保罗研究基金会;

关键词：

finite group; solvable group; almost simple group; Gruenberg-Kegel graph (prime graph); PRIME GRAPH;

D O I：

10.1007/s10469-018-9484-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the Gruenberg-Kegel graph of a finite almost simple group is equal to the Gruenberg-Kegel graph of some finite solvable group if it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg-Kegel graphs contain no 3-cocliques.

引用

页码：115 / 129

页数：15

共 16 条

[1]

[Anonymous], MEMOIRS AMS

[2]

[Anonymous], 1870, NOUV ANN MATH

[3] Spectra of finite linear and unitary groups [J].

Buturlakin, A. A. .

ALGEBRA AND LOGIC, 2008, 47 (02) :91-99

[4]

Conway J. H., 1985, MATHBB ATLAS FINITE

[5]

Gorenstein D., 1968, Harper's Ser. Modern Math.

[6] A characterization of the prime graphs of solvable groups [J].

Gruber, Alexander ;

Keller, Thomas Michael ;

Lewis, Mark L. ;

Naughton, Keeley ;

Strasser, Benjamin .

JOURNAL OF ALGEBRA, 2015, 442 :397-422

[7]

Harary F., 1969, ADDISON WESLEY SER M

[8]

Higman G., 1957, J.London Math. Soc. (2), V32, P335, DOI DOI 10.1112/JLMS/S1-32.3.335

[9]

Kleidman P.B., 1990, London Math. Soc. Lecture Note Ser., V129

[10] Recognition of alternating groups of prime degree from their element orders [J].

Kondrat'ev, AS ;

Mazurov, VD .

SIBERIAN MATHEMATICAL JOURNAL, 2000, 41 (02) :294-302

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