Recognition of finite simple groups S4(q) by their element orders

被引:67
作者
Mazurov V.D.
机构
基金
俄罗斯基础研究基金会;
关键词
Finite simple groups; Recognizability of groups by their element orders;
D O I
10.1023/A:1015356614025
中图分类号
学科分类号
摘要
It is proved that among simple groups S4(q) in the class of finite groups, only the groups S4(3n), where n is an odd number greater than unity, are recognizable by a set of their element orders. It is also shown that simple groups U3(9), 3D 4(2), G2(4), S6(3), F4(2); and 2E6(2) are recognizable, but L3(3) is not. © 2002 Plenum Publishing Corporation.
引用
收藏
页码:93 / 110
页数:17
相关论文
共 17 条
[1]  
Mazurov V.D., Xu M.C., Cao H.P., Recognition of finite simple groups L<sub>3</sub>(2<sup>m</sup>) and U<sub>3</sub>(2<sup>m</sup>) by their element orders, Algebra Logika, 39, 5, pp. 567-585, (2000)
[2]  
Williams J.S., Prime graph components of finite groups, J. Alg., 69, 2, pp. 487-513, (1981)
[3]  
Kondratiev A.S., Mazurov V.D., Recognition of alternating groups of prime degree from their element orders, Sib. Mat. Zh., 41, 2, pp. 360-371, (2000)
[4]  
Thompson J.G., Normal p-complements for finite groups, Math. Z., 72, 2, pp. 332-354, (1960)
[5]  
Zassenhaus H., Kennzeichnung endlichen linearen Gruppen als Permutationsgruppen, Abh. Math. Sem. Univ. Hamb., 11, pp. 17-40, (1936)
[6]  
Zassenhaus H., Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamb., 11, pp. 187-220, (1936)
[7]  
Mazurov V.D., Characterizations of finite groups by sets of orders of their elements, Algebra Logika, 36, 1, pp. 37-53, (1997)
[8]  
Zsigmondi K., Zur Theorie der Potenzreste, Monatsh. Math. Phys., 3, pp. 265-284, (1892)
[9]  
Jansen C., Lux K., Parker R., Wilson R., An Atlas of Brauer Characters, (1985)
[10]  
Brauer R., Nesbitt C., On the Modular Representations of Groups of Finite Order, I, Univ. Toronto Stud., Math. Ser., 4, (1937)