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Groups of prime power order. Volume 1 /
This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathemati...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; New York :
W. de Gruyter,
©2008.
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| Colección: | De Gruyter expositions in mathematics ;
46. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Frontmatter; Contents; List of definitions and notations; Foreword; Preface; Introduction; 1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia; 2. The class number, character degrees; 3. Minimal classes; 4. p-groups with cyclic Frattini subgroup; 5. Hall's enumeration principle; 6. q'-automorphisms of q-groups; 7. Regular p-groups; 8. Pyramidal p-groups; 9. On p-groups of maximal class; 10. On abelian subgroups of p-groups; 11. On the power structure of a p-group; 12. Counting theorems for p-groups of maximal class; 13. Further counting theorems.
- 14. Thompson's critical subgroup; 15. Generators of p-groups; 16. Classification of finite p-groups all of whose noncyclic subgroups are normal; 17. Counting theorems for regular p-groups; 18. Counting theorems for irregular p-groups; 19. Some additional counting theorems; 20. Groups with small abelian subgroups and partitions; 21. On the Schur multiplier and the commutator subgroup; 22. On characters of p-groups; 23. On subgroups of given exponent; 24. Hall's theorem on normal subgroups of given exponent; 25. On the lattice of subgroups of a group; 26. Powerful p-groups.
- 27. p-groups with normal centralizers of all elements; 28. p-groups with a uniqueness condition for nonnormal subgroups; 29. On isoclinism; 30. On p-groups with few nonabelian subgroups of order pp and exponent p; 31. On p-groups with small p0-groups of operators; 32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups; 33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3; 34. Nilpotent groups of automorphisms; 35. Maximal abelian subgroups of p-groups; 36. Short proofs of some basic characterization theorems of finite p-group theory.
- 37. MacWilliams' theorem; 38. p-groups with exactly two conjugate classes of subgroups of small orders and exponent p>2; 39. Alperin's problem on abelian subgroups of small index; 40. On breadth and class number of p-groups; 41. Groups in which every two noncyclic subgroups of the same order have the same rank; 42. On intersections of some subgroups; 43. On 2-groups with few cyclic subgroups of given order; 44. Some characterizations of metacyclic p-groups; 45. A counting theorem for p-groups of odd order; Appendix 1. The Hall-Petrescu formula.
- Appendix 2. Mann's proof of monomiality of p-groups; Appendix 3. Theorems of Isaacs on actions of groups; Appendix 4. Freiman's number-theoretical theorems; Appendix 5. Another proof of Theorem 5.4; Appendix 6. On the order of p-groups of given derived length; Appendix 7. Relative indices of elements of p-groups; Appendix 8. p-groups withabsolutely regular Frattini subgroup; Appendix 9. On characteristic subgroups of metacyclic groups; Appendix 10. On minimal characters of p-groups; Appendix 11. On sums of degrees of irreducible characters.