Quasirecognizability by the set of element orders for groups 3D4(q), for q even

被引:6
作者
Alekseeva O.A. [1 ]
机构
[1] Chelyabinsk Humanitarian Institute, Chelyabinsk
关键词
Finite group; Prime graph; Quasirecognizability; Set of element orders; Simple group;
D O I
10.1007/s10469-006-0001-z
中图分类号
学科分类号
摘要
It is proved that if G is a finite group with an element order set as in the simple group 3D4(q), where q is even, then the commutant of G/F(G) is isomorphic to 3D4(q) and the factor group G/G′ is a cyclic {2, 3}-group. © 2006 Springer Science+Business Media, Inc.
引用
收藏
页码:1 / 11
页数:10
相关论文
共 18 条
[1]  
Williams J.S., Prime graph components of finite groups, J. Alg., 69, 2, pp. 487-513, (1981)
[2]  
Kondratiev A.S., Prime graph components of finite simple groups, Mat. 56., 180, 6, pp. 787-797, (1989)
[3]  
Mazurov V.D., Recognition of finite simple groups S<sub>4</sub>(q) by their element orders, Algebra Logika, 41, 2, pp. 166-198, (2002)
[4]  
Unsolved Problems in Group Theory, the Kourovka Notebook, 15th Edn., (2002)
[5]  
Alekseeva O.A., Kondratiev A.S., Recognizing group e<sub>8</sub>(q) by the set of element orders, Ukr. Mat. Zh., 54, 7, pp. 1003-1008, (2002)
[6]  
Alekseeva O.A., Kondratiev A.S., Quasirecognizability of a class of finite simple groups by the set of element orders, Sib. Math. Zh., 44, 2, pp. 241-255, (2003)
[7]  
Vasilyev A.V., Grechkoseeva M.A., Recognizability of finite simple orthogonal groups in dimensions 2 <sup>m</sup>, 2<sup>m</sup> + 1, and 2<sup>m</sup> + 2, Sib. Math. Zh., 45, 3, pp. 510-526, (2004)
[8]  
Alekseeva O.A., Kondratiev A.S., Quasirecognizability by the set of element orders for groups<sup>3</sup> D<sub>4</sub>(q) and F<sub>4</sub>(q), for q odd, Algebra Logika, 44, 5, pp. 517-539, (2005)
[9]  
Aschbacher M., Finite Group Theory, (1986)
[10]  
Conway J., Curtis R., Norton S., Et al., Atlas of Finite Groups, (1985)