Finite group theory

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Finite group theory / M. Aschbacher

版:: 2nd ed
資料種別:: 図書
出版情報:: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 2000
形態:: xi, 304 p. ; 24 cm
シリーズ名:: Cambridge studies in advanced mathematics ; 10 <BA00109761>
著者名:: Aschbacher, Michael, 1944- <DA00189053>
ISBN:: 9780521781459 [0521781450] (: hbk)
9780521786751 [0521786754] (: pbk)
書誌ID:: BA48144943

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注記:

Includes bibliographical references and index

主題:

Finite groups

言語:

英語

目次情報:

Preface

Preliminary results / 1：

Elementary group theory

Categories / 2：

Graphs and geometries / 3：

Abstract representations / 4：

Permutation representations

Sylow's Theorem / 5：

Representations of groups on groups

Normal series / 7：

Characteristic subgroups and commutators / 8：

Solvable and Nilpotent groups / 9：

Semidirect products / 10：

Central products and wreath products / 11：

Linear representations

Modules over the group ring / 12：

The general linear group and special linear group / 13：

The dual representation / 14：

Permutation groups

The symmetric and alternating groups / 15：

Rank 3 permutation groups / 16：

Extensions of groups and modules

1-cohomology / 17：

Coprime action / 18：

Spaces with forms

Bilinear, sesquilinear, and quadratic forms / 19：

Witt's Lemma / 20：

Spaces over finite fields / 21：

The classical groups / 22：

p-groups

Extremal p-groups / 23：

Coprime action on p-groups / 24：

Change of field of a linear representation

Tensor products / 25：

Representations over finite fields / 26：

Minimal polynomials / 27：

Presentations of groups

Free groups / 28：

Coxeter groups / 29：

Root systems / 30：

The generalized Fitting subgroup

Thompson factorization / 31：

Central extensions / 33：

Linear representations of finite groups

Characters in coprime characteristic / 34：

Characters in characteristic zero / 35：

Some special actions / 36：

Transfer and fusion

Transfer / 37：

Alperin's Fusion Theorem / 38：

Normal p-complements / 39：

Semiregular action / 40：

The geometry of groups of Lie type

Complexes / 41：

Buildings / 42：

BN-pairs and Tits systems / 43：

Signalizer functors

Solvable signalizer functors / 44：

Finite simple groups

Involutions in finite groups / 45：

Connected groups / 46：

The finite simple groups / 47：

An outline of the Classification Theorem / 48：

References

List of Symbols

Index

Preface

Preliminary results / 1：

Elementary group theory

Categories / 2：

Graphs and geometries / 3：

Abstract representations / 4：

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