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Simplicial subdivisions and the chromatic number of a group

  • Leonard Wienke
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Elementary Theory of Groups and Group Rings, and Related Topics
This chapter is in the book Elementary Theory of Groups and Group Rings, and Related Topics

Abstract

We give an overview on simplicial subdivision theory and its role in current research. We then specialize to chromatic subdivisions and define the notion of chromatic groups. We state conjectures and open problems concerning the topics involved.

Abstract

We give an overview on simplicial subdivision theory and its role in current research. We then specialize to chromatic subdivisions and define the notion of chromatic groups. We state conjectures and open problems concerning the topics involved.

Chapters in this book

  1. Frontmatter I
  2. Introduction V
  3. Conference booklet and talks VII
  4. Remembrances of Gilbert XI
  5. Contents XXIX
  6. Explicit universal axioms for Kaplansky groups 1
  7. Isoperimetric and isodiametric functions of group extensions 7
  8. The homology of groups, profinite completions, and echoes of Gilbert Baumslag 11
  9. Some properties of the Baumslag groups G(m, n) 29
  10. Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory 33
  11. Some model theory of the Heisenberg group: II. The three generator case 47
  12. On vector-valued Hecke forms 53
  13. Two algorithms in group theory 73
  14. On products of closed subsets in free groups 81
  15. Misbehaved direct products 85
  16. A survey on Albert algebras and groups of type F4 89
  17. Perspectives on p-ary bent functions 103
  18. Multilinear cryptography using nilpotent groups 127
  19. Musings on generic-case complexity 135
  20. Noncommutative Gebauer–Möller criteria 149
  21. On the numbers of the form x2 + 11y2 177
  22. Separability properties of nilpotent ℚ[x]-powered groups 203
  23. Infinite nested radicals 219
  24. Commutative transitivity property in groups and Lie algebras 225
  25. Simplicial subdivisions and the chromatic number of a group 233
https://doi.org/10.1515/9783110638387-020

Chapters in this book

  1. Frontmatter I
  2. Introduction V
  3. Conference booklet and talks VII
  4. Remembrances of Gilbert XI
  5. Contents XXIX
  6. Explicit universal axioms for Kaplansky groups 1
  7. Isoperimetric and isodiametric functions of group extensions 7
  8. The homology of groups, profinite completions, and echoes of Gilbert Baumslag 11
  9. Some properties of the Baumslag groups G(m, n) 29
  10. Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory 33
  11. Some model theory of the Heisenberg group: II. The three generator case 47
  12. On vector-valued Hecke forms 53
  13. Two algorithms in group theory 73
  14. On products of closed subsets in free groups 81
  15. Misbehaved direct products 85
  16. A survey on Albert algebras and groups of type F4 89
  17. Perspectives on p-ary bent functions 103
  18. Multilinear cryptography using nilpotent groups 127
  19. Musings on generic-case complexity 135
  20. Noncommutative Gebauer–Möller criteria 149
  21. On the numbers of the form x2 + 11y2 177
  22. Separability properties of nilpotent ℚ[x]-powered groups 203
  23. Infinite nested radicals 219
  24. Commutative transitivity property in groups and Lie algebras 225
  25. Simplicial subdivisions and the chromatic number of a group 233
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