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 o
Computing the Subgroups of a Permutation Group
โ Scribed by John J. Cannon; Bruce C. Cox; Derek F. Holt
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 279 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
โฆ Synopsis
A new method for computing the conjugacy classes of subgroups of a finite group is described.
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## 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
This article describes an algorithm for computing up to conjugacy all subgroups of a finite solvable group that are invariant under a set of automorphisms. It constructs the subgroups stepping down along a normal chain with elementary abelian factors.