Topic
Simple group
About: Simple group is a research topic. Over the lifetime, 3992 publications have been published within this topic receiving 72142 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 1972TL;DR: In this article, the authors present a generalization of the Weyl Group to the Chevalley Group, and further properties of the twisted simple groups, including generators, relations and automorphisms.
Abstract: Partial table of contents: The Classical Simple Groups. Weyl Groups. Simple Lie Algebras. The Chevalley Groups. Unipotent Subgroups. The Diagonal and Monomial Subgroups. The Bruhat Decomposition. Polynomial Invariants of the Weyl Group. The Exponents of the Weyl Group. Further Properties of the Chevalley Groups. Generators, Relations and Automorphisms in Chevalley Groups. The Twisted Simple Groups. Further Properties of the Twisted Groups. Associated Geometrical Structures. Sporadic Simple Groups. Bibliography. Index of Notation. Index.
1,792 citations
TL;DR: In this article, the results gathered here on simple Lie algebras have been selected with attention to the needs of unified model builders who study Yang-Mills theories based on simple, local symmetry groups that contain as a subgroup the SUw2 × Uw1 × SUc3 symmetry of the standard theory of electromagnetic, weak, and strong interactions.
1,651 citations
Book•
21 Aug 2008
TL;DR: In this article, a unified treatment of the theory of geometric subgroups of the classical groups, introduced by Aschbacher, is presented, and the questions of maximality and conjugacy of these groups are answered.
Abstract: With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.
1,551 citations
1 Jan 1995
1,449 citations
Book•
1 Jan 1955
TL;DR: In this article, the authors define the notion of permutation groups as a group of linear substitutions, and show that a group can be represented as a permutation-group.
Abstract: Preface to the second edition Preface to the first edition 1. On permutations 2. The definition of a group 3. On the simpler properties of a group which are independent of its mode of representation 4. Further properties of a group which are independent of its mode of representation 5. On the composition-series of a group 6. On the isomorphism of a group within itself 7. On Abelian groups 8. On groups whose orders are the powers of primes 9. On Sylow's theorem 10. On permutation-groups: transitive and intransitive groups 11. On permutation-groups: transitivity and primitivity 12. On the representation of a group of finite order as a permutation-group 13. On groups of linear substitutions 14. On the representation of a group of finite order as a group of linear substitutions 15. On group-characteristics 16. Some applications of the theory of groups of linear substitutions and of group-characteristics 17. On the invariants of groups of linear substitutions 18. On the graphical representation of a group 19. On the graphical representation of groups 20. On congruence groups Notes Index of technical terms Index of authors quoted General index.
1,226 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 10 |
| 2024 | 27 |
| 2023 | 44 |
| 2022 | 80 |
| 2021 | 129 |
| 2020 | 124 |