ONE COROLLARY OF THE DESCRIPTION OF FINITE GROUPS WITHOUT ELEMENTS OF ORDER 6

被引:1
作者
Kondrat'ev, Anatoly Semenovich [1 ,2 ]
Nirova, Marina Sefovna [3 ]
机构
[1] RAS, UB, NN Krasovskii Inst Math & Mech, S Kovalevskaya St 16, Ekaterinburg 620108, Russia
[2] Ural Fed Univ, Ural Matemat Ctr, Mira St 19, Ekaterinburg 620002, Russia
[3] Kabardino Balkarian State Univ, Chernyshevsky St 175, Nalchik 360004, Russia
来源
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2023年 / 20卷 / 02期
关键词
finite group; non-solvable group; Gruenberg-Kegel graph; PRIME GRAPH COMPONENTS;
D O I
10.33048/semi.2023.20.052
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a finite group. The set of all prime divisors of the order of G is denoted by p(G). The Gruenberg-Kegel graph (the prime graph) G pi(G) of G is defined as the graph with the vertex set pi (G) in which two different vertices p and q are adjacent if and only if G contains an element of order pq. If the order of G is even, then p1(G) denotes the connected component of G(G) containing 2. It is actual the problem of describing finite groups with disconnected Gruenberg-Kegel graphs. In the present article, all finite non-solvable groups G with 3 is an element of p(G)\pi(1)(G) are determined.
引用
收藏
页码:854 / 858
页数:5
相关论文
共 16 条
[1]   Classification of finite groups with a CC-subgroup [J].
Arad, Z ;
Herfort, W .
COMMUNICATIONS IN ALGEBRA, 2004, 32 (06) :2087-2098
[2]  
Bray JN, 2013, LOND MATH S, V407, P1, DOI 10.1017/CBO9781139192576
[3]  
CONWAY JS, 1985, ALA AGR EXP STA BULL, P1
[4]  
Corrigenda, 1996, J. Algebra, V181, P659
[5]  
Gorenstein D., 1968, Finite Groups
[6]  
Gorenstein D., 1998, The classifcation of the finite simple groups, Number 3, Part I, Chapter A: Almost simple K-groups
[7]  
Higman G., 1968, Lecture Notes of University of Michigan
[8]   PRIME GRAPH COMPONENTS OF THE SIMPLE-GROUPS OF LIE TYPE OVER THE FIELD OF EVEN CHARACTERISTIC [J].
IIYORI, N ;
YAMAKI, H .
JOURNAL OF ALGEBRA, 1993, 155 (02) :335-343
[9]   Finite Groups without Elements of Order Six [J].
Kondrat'ev, A. S. ;
Minigulov, N. A. .
MATHEMATICAL NOTES, 2018, 104 (5-6) :696-701
[10]   Finite Groups with Given Properties of Their Prime Graphs [J].
Kondrat'ev, A. S. .
ALGEBRA AND LOGIC, 2016, 55 (01) :77-82