Author | Robinson, Derek J. S. author |
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Title | A Course in the Theory of Groups [electronic resource] / by Derek J. S. Robinson |
Imprint | New York, NY : Springer US, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0128-8 |
Descript | XVII, 481 p. online resource |
1 Fundamental Concepts of Group Theory -- 1.1 Binary Operations, Semigroups, and Groups -- 1.2 Examples of Groups -- 1.3 Subgroups and Cosets -- 1.4 Homomorphisms and Quotient Groups -- 1.5 Endomorphisms and Automorphisms -- 1.6 Permutation Groups and Group Actions -- 2 Free Groups and Presentations -- 2.1 Free Groups -- 2.2 Presentations of Groups -- 2.3 Varieties of Groups -- 3 Decompositions of a Group -- 3.1 Series and Composition Series -- 3.2 Some Simple Groups -- 3.3 Direct Decompositions -- 4 Abelian Groups -- 4.1 Torsion Groups and Divisible Groups -- 4.2 Direct Sums of Cyclic and Quasicyclic Groups -- 4.3 Pure Subgroups and p-groups -- 4.4 Torsion-free Groups -- 5 Soluble and Nilpotent Groups -- 5.1 Abelian and Central Series -- 5.2 Nilpotent Groups -- 5.3 Groups of Prime-Power Order -- 5.4 Soluble Groups -- 6 Free Groups and Free Products -- 6.1 Further Properties of Free Groups -- 6.2 Free Products of Groups -- 6.3 Subgroups of Free Products -- 6.4 Generalized Free Products -- 7 Finite Permutation Groups -- 7.1 Multiple Transitivity -- 7.2 Primitive Permutation Groups -- 7.3 Classification of Sharply k-transitive Permutation Groups -- 7.4 The Mathieu Groups -- 8 Representations of Groups -- 8.1 Representations and Modules -- 8.2 Structure of the Group Algebra -- 8.3 Characters -- 8.4 Tensor Products and Representations -- 8.5 Applications to Finite Groups -- 9 Finite Soluble Groups -- 9.1 Hall ?-subgroups -- 9.2 Sylow Systems and System Normalizers -- 9.3 p-soluble Groups -- 9.4 Supersoluble Groups -- 9.5 Formations -- 10 The Transfer and Its Applications -- 10.1 The Transfer Homomorphism -- 10.2 Grรผnโs Theorems -- 10.3 Frobeniusโ Criterion for p-nilpotence -- 10.4 Thompsonโs Criterion for p-nilpotene -- 10.5 Fixed-point-free Automorphisms -- 11 The Theory of Group Extensions -- 11.1 Group Extensions and Covering Groups -- 11.2 Homology Groups and Cohomology Groups -- 11.3 The Gruenberg Resolution -- 11.4 Group-theoretic Interpretations of the (Co)homology Groups -- 12 Generalizations of Nilpotent and Soluble Groups -- 12.1 Locally Nilpotent Groups -- 12.2 Some Special Types of Locally Nilpotent Groups -- 12.3 Engel Elements and Engel Groups -- 12.4 Classes of Groups Defined by General Series -- 12.5 Locally Soluble Groups -- 13 Subnormal Subgroups -- 13.1 Joins and Intersections of Subnormal Subgroups -- 13.2 Permutability and Subnormality -- 13.3 The Minimal Condition on Subnormal Subgroups -- 13.4 Groups in Which Normality Is a Transitive Relation -- 13.5 Automorphism Towers and Complete Groups -- 14 Finiteness Properties -- 14.1 Finitely Generated Groups and Finitely Presented Groups -- 14.2 Torsion Groups and the Burnside Problems -- 14.3 Locally Finite Groups -- 14.4 2-groups with the Maximal or Minimal Condition -- 14.5 Finiteness Properties of Conjugates and Commutators -- 15 Infinite Soluble Groups -- 15.1 Soluble Linear Groups -- 15.2 Soluble Groups with Finiteness Conditions on Abelian Subgroups -- 15.3 Finitely Generated Soluble Groups and the Maximal Condition on Normal Subgroups -- 15.4 Finitely Generated Soluble Groups and Residual Finiteness -- 15.5 Finitely Generated Soluble Groups and Their Frattini Subgroups