Preliminaries / 1: |
Commutators / 1.1: |
Basic theory of finite p-groups / 1.2: |
Local fields / 1.3: |
New groups from old / 2: |
Group actions and extensions / 2.1: |
Pull-backs and central products / 2.2: |
Wreath products, imprimitivity and actions on trees / 2.3: |
Iterated wreath products of C[subscript p] / 2.4: |
p-groups of maximal class / 3: |
Definition and examples of p-groups of maximal class / 3.1: |
The degree of commutativity of p-groups of maximal class / 3.2: |
The power structure of p-groups of maximal class / 3.3: |
Bounding the degree of commutativity / 3.4: |
Finite p-groups acting uniserially / 4: |
Uniserial actions on finite p-groups / 4.1: |
Wreath products and uniserial action / 4.2: |
Uniserial action on finite abelian p-groups / 4.3: |
The Sylow p-subgroups of GL(d, Z/p[superscript n]Z) / 4.4: |
The maximal p-subgroups of GL(d, Z) / 4.5: |
Using Lie algebra theory to find bounds / 5: |
Preliminaries on Lie algebras / 5.1: |
Jacobson's version of Engel's theorem / 5.2: |
Application to p-groups of maximal class / 5.3: |
Settled p-groups / 5.4: |
Automorphisms with p fixed points / 5.5: |
The proof of Conjecture A using powerful p-groups / 6: |
Powerful p-groups / 6.1: |
Strongly hereditarily powerful subgroups / 6.2: |
Application to p-groups of small coclass / 6.3: |
Conjecture A / 6.4: |
Pro-p-groups / 7: |
Topological groups / 7.1: |
Pro-finite groups / 7.2: |
Free groups / 7.3: |
Pro-p-groups of finite coclass / 7.4: |
Constructing finite p-groups / 8: |
Realizations and twistings / 8.1: |
Constructing p-groups of maximal class / 8.2: |
Twisting homomorphisms for p-groups of maximal class / 8.3: |
Constructible p-groups / 8.4: |
Homological algebra / 9: |
Derived functors / 9.1: |
Double complexes and spectral sequences / 9.2: |
Ext and Tor / 9.3: |
The homology and cohomology of groups / 9.4: |
Interpretations of group homology and cohomology / 9.5: |
Uniserial p-adic space groups / 10: |
Primitive p-adic representations / 10.1: |
The maximal irreducible p-subgroups of GL(d, Q[subscript p]) / 10.2: |
Lattices for uniserial p-adic space groups / 10.3: |
Embedding in a split space group / 10.4: |
Bounding the coclass of uniserial 2-adic space groups / 10.5: |
The structure of finite p-groups / 11: |
Properties of settled p-groups / 11.1: |
Preliminary structure theorems and generic bounds / 11.2: |
Structure theorems for p-groups of coclass r / 11.3: |
Calculating the twisting homomorphisms / 11.4: |
Beyond coclass / 12: |
Finiteness conditions on pro-p-groups / 12.1: |
p-groups of rank 3, width 2 and obliquity 0 / 12.2: |
The Grigorchuk group / 12.3: |
The Nottingham group / 12.4: |
Bibliography |
Symbol index |
Index |
Preliminaries / 1: |
Commutators / 1.1: |
Basic theory of finite p-groups / 1.2: |
Local fields / 1.3: |
New groups from old / 2: |
Group actions and extensions / 2.1: |