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Fast recognition of doubly transitive groups

โœ Scribed by P.J. Cameron; J. Cannon

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
852 KB
Volume
12
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

Primitive groups with most suborbits dou
Primitive groups with most suborbits doubly transitive
โœ Peter J. Cameron ๐Ÿ“‚ Article ๐Ÿ“… 1973 ๐Ÿ› Springer ๐ŸŒ English โš– 539 KB

Jz of order 175560 has a primitive rank 5 representation of degree 266 in which the stabiliser of a point is isomorphic to PSL (2, 11) and acts doubly transitively on suborbits of lengths 11 and 12; the other suborbit lengths are 110 and 132. (See Livingstone [7].) Note also that the group [Z5 xZs]S