The structure of groups of prime power order

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The structure of groups of prime power order / C.R. Leedham-Green and S. McKay

資料種別:

図書

出版情報:

Oxford ; New York : Oxford University Press, 2002

形態:

xii, 334 p. ; 24 cm

シリーズ名:

London Mathematical Society monographs ; new ser., 27 <BA00134328>
Oxford science publications <BA00281843>

著者名:

ISBN:

9780198535485 [0198535481]

書誌ID:

BA58443124

子書誌情報

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他の版・巻

書誌詳細

注記:

Includes bibliographical references and indexes

主題:

Automorphisms; Finite groups

言語:

英語

目次情報:

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：

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