๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Computing Sylow Subgroups in Permutation Groups

โœ Scribed by JOHN CANNON; BRUCE COX; DEREK HOLT

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
371 KB
Volume
24
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

โœฆ Synopsis

We describe the theory and implementation of a practical algorithm for computing a Sylow subgroup of a permutation group and for finding an element that conjugates one Sylow subgroup to another. The performance of the current implementations in the Magma system represents a significant improvement on previous implementations for many important classes of examples and generally extends the range of realistic applicability to groups of much larger degrees than before.

๐Ÿ“œ SIMILAR VOLUMES

Sylow Permutable Subnormal Subgroups of
Sylow Permutable Subnormal Subgroups of Finite Groups
โœ A. Ballester-Bolinches; R. Esteban-Romero ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 104 KB

## dedicated to john cossey on the occasion of his 60th birthday An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every subnormal subgrou

Computing the Subgroups of a Permutation
Computing the Subgroups of a Permutation Group
โœ John J. Cannon; Bruce C. Cox; Derek F. Holt ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 279 KB

A new method for computing the conjugacy classes of subgroups of a finite group is described.

Sylow Subgroups in Parallel
Sylow Subgroups in Parallel
โœ William M Kantor; Eugene M Luks; Peter D Mark ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 389 KB

Sylow subgroups are fundamental in the design of asymptotically efficient group-theoretic algorithms, just as they have been in the study of the structure of ลฝ . finite groups. We present efficient parallel NC algorithms for finding and conjugating Sylow subgroups of permutation groups, as well as f

Transitive Subgroups of Primitive Permut
Transitive Subgroups of Primitive Permutation Groups
โœ Martin W. Liebeck; Cheryl E. Praeger; Jan Saxl ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 492 KB

to helmut wielandt on the occasion of his 90th birthday We investigate the finite primitive permutation groups G which have a transitive subgroup containing no nontrivial subnormal subgroup of G. The conclusion is that such primitive groups are rather rare, and that their existence is intimately co