A Note on the Adjacency Criterion for the Prime Graph and the Characterization of Cp(3)

被引：6

作者：

He, Huaiyu ^{[2
]}

Shi, Wujie ^{[1
]}

机构：

[1] Chongqing Univ Arts & Sci, Sch Math & Stat, Chongqing 402160, Peoples R China

[2] Shanghai Univ Polit Sci & Law, Dept Econ & Management, Shanghai 201701, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2012年 / 19卷 / 03期

关键词：

recognition; spectrum; simple group; prime graph; FINITE; RECOGNITION;

D O I：

10.1142/S1005386712000429

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we remedy some errors in the paper [17]; in particular, for any non-abelian finite simple group G other than Alt(n) such that n - 2, n - 1 and n are not primes, we prove that for each r is an element of pi(G), there always exists s is an element of pi(G) which is non-adjacent to r in the Gruenberg-Kegel graph of G. Applications of these results to the recognition problem of some finite simple groups by spectrum are also considered.

引用

页码：553 / 562

页数：10

共 19 条

[1]

CARTER RW, 1972, COMPOS MATH, V25, P1

[2] Recognition of the finite almost simple groups PGL2(q) by their spectrum [J].

Chen, G. Y. ;

Mazurov, V. D. ;

Shi, W. J. ;

Vasil'ev, A. V. ;

Zhurtov, A. Kh. .

JOURNAL OF GROUP THEORY, 2007, 10 (01) :71-85

[3] On minimal permutation representations of classical simple groups [J].

Grechkoseeva, MA .

SIBERIAN MATHEMATICAL JOURNAL, 2003, 44 (03) :443-462

[4] Finite simple unisingular groups of Lie type [J].

Guralnick, RM ;

Tiep, PH .

JOURNAL OF GROUP THEORY, 2003, 6 (03) :271-310

[5] Prime power graphs for groups of Lie type [J].

Kantor, WM ;

Seress, K .

JOURNAL OF ALGEBRA, 2002, 247 (02) :370-434

[6] r-Recognizability of Bn(q) and Cn(q) where n=2m≥4 [J].

Khosravi, A ;

Khosravi, B .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2005, 199 (1-3) :149-165

[7]

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

[8]

LIEBECK MW, 1990, MEM AM MATH SOC, V86, P1

[9]

Lipschutz S, 2000, PROG NAT SCI, V10, P11

[10]

Lucido MS, 1999, P MATH SEMINAR U PAD, V102, P1

← 1 2 →