FAST RECOGNITION OF DOUBLY TRANSITIVE GROUPS

被引：2

作者：

CAMERON, PJ ^{[1
]}

CANNON, J ^{[1
]}

机构：

[1] UNIV SYDNEY,SCH MATH & STAT,SYDNEY,NSW 2006,AUSTRALIA

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 1991年 / 12卷 / 4-5期

关键词：

D O I：

10.1016/S0747-7171(08)80098-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The availability of the classification of finite simple groups allows us to design algorithms for identifying the composition factors of finite groups. This paper presents an algorithm which identifies any finite doubly transitive permutation group G. If we exclude the 2-transitive subgroups of the one-dimensional affine group and 14 small exceptional groups, the cost of our algorithm is essentially the cost of constructing a base and strong generating set for G. Consequently, our algorithm avoids the need to compute the soluble residual of G as required by Kantor's composition factors algorithm for a general permutation group. © 1991, Academic Press Limited. All rights reserved.

引用

页码：459 / 474

页数：16

共 16 条

[1]

BUTLER G, 1982, MATH COMPUT, V39, P633

[2] FINITE PERMUTATION-GROUPS AND FINITE SIMPLE-GROUPS [J].

CAMERON, PJ .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1981, 13 (JAN) :1-22

[3]

Cannon J.J., 1984, COMPUTATIONAL GROUP, P145

[4]

CANNON JJ, 1984, 1983 1984 P RUTG GRO, P1

[5] 2-TRANSITIVE PERMUTATION REPRESENTATIONS OF FINITE CHEVALLEY GROUPS [J].

CURTIS, CW ;

KANTOR, WM ;

SEITZ, GM .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 218 (APR) :1-59

[6]

Gorenstein D., 1982, FINITE SIMPLE GROUPS

[7]

Hering C., 1974, GEOMETRIAE DEDICATA, V2, P425

[8] DEGREES OF STEINBERG CHARACTERS OF CHEVALLEY GROUPS [J].

HOWLETT, RB .

MATHEMATISCHE ZEITSCHRIFT, 1974, 135 (02) :125-135

[9]

Huppert B, 1957, MATH Z, V68, P126

[10] A COMPACT REPRESENTATION FOR PERMUTATION-GROUPS [J].

JERRUM, M .

JOURNAL OF ALGORITHMS, 1986, 7 (01) :60-78

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