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1.

図書
図書
1. Enumeration of finite groups (: hbk.)
Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman
出版情報: Cambridge : Cambridge University Press, 2007  xii, 281 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 173
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Preface
Introduction / 1：
Elementary Results / I：
Some basic observations / 2：
Groups of Prime Power Order / II：
Preliminaries / 3：
Tensor products and exterior squares of abelian groups / 3.1：
Commutators and nilpotent groups / 3.2：
The Frattini subgroup / 3.3：
Linear algebra / 3.4：
Enumerating p-groups: a lower bound / 4：
Relatively free groups / 4.1：
Proof of the lower bound / 4.2：
Enumerating p-groups: upper bounds / 5：
An elementary upper bound / 5.1：
An overview of the Sims approach / 5.2：
'Linearising' the problem / 5.3：
A small set of relations / 5.4：
Proof of the upper bound / 5.5：
Pyber's Theorem / III：
Some more preliminaries / 6：
Hall subgroups and Sylow systems / 6.1：
The Fitting subgroup / 6.2：
Permutations and primitivity / 6.3：
Group extensions and cohomology / 7：
Group extensions / 7.1：
Cohomology / 7.2：
Restriction and transfer / 7.3：
The McIver and Neumann bound / 7.4：
Some representation theory / 8：
Semisimple algebras / 8.1：
Clifford's theorem / 8.2：
The Skolem-Noether theorem / 8.3：
Every finite skew field is a field / 8.4：
Primitive soluble linear groups / 9：
Some basic structure theory / 9.1：
The subgroup B / 9.2：
The orders of groups / 10：
Conjugacy classes of maximal soluble subgroups of symmetric groups / 11：
Enumeration of finite groups with abelian Sylow subgroups / 12：
Counting soluble A-groups: an overview / 12.1：
Soluble A-subgroups of the general linear group and the symmetric groups / 12.2：
Maximal soluble p'-A-subgroups / 12.3：
Enumeration of soluble A-groups / 12.4：
Maximal soluble linear groups / 13：
The field K and a subfield of K / 13.1：
The quotient G/C and the algebra / 13.2：
The quotient B/A / 13.3：
Structure of G determined by B / 13.4：
Conjugacy classes of maximal soluble subgroups of the general linear groups / 14：
Pyber's theorem: the soluble case / 15：
Extensions and soluble subgroups / 15.1：
Pyber's theorem / 15.2：
Pyber's theorem: the general case / 16：
Three theorems on group generation / 16.1：
Universal central extensions and covering groups / 16.2：
The generalised Fitting subgroup / 16.3：
The general case of Pyber's theorem / 16.4：
Other Topics / IV：
Enumeration within varieties of abelian groups / 17：
Varieties of abelian groups / 17.1：
Enumerating partitions / 17.2：
Further results on abelian groups / 17.3：
Enumeration within small varieties of A-groups / 18：
A minimal variety of A-groups / 18.1：
The join of minimal varieties / 18.2：
Enumeration within small varieties of p-groups / 19：
Enumerating two small varieties / 19.1：
The ratio of two enumeration functions / 19.2：
Miscellanea / 20：
Enumerating d-generator groups / 20.1：
Groups with few non-abelian composition factors / 20.2：
Enumerating graded Lie rings / 20.3：
Groups of nilpotency class 3 / 20.4：
Survey of other results / 21：
Graham Higman's PORC conjecture / 21.1：
Isoclinism classes of p-groups / 21.2：
Groups of square-free order / 21.3：
Groups of cube-free order / 21.4：
Groups of arithmetically small orders / 21.5：
Surjectivity of the enumeration function / 21.6：
Densities of certain sets of group orders / 21.7：
Enumerating perfect groups / 21.8：
Some open problems / 22：
Maximising two functions / Appendix A：
References
Index
Preface
Introduction / 1：
Elementary Results / I：
2.

図書
図書
2. Tool and object : a history and philosophy of category theory
Ralf Krömer
出版情報: Basel : Birkhäuser, c2007  xxxvi, 367 p. ; 24 cm
シリーズ名: Science networks, historical studies ; v. 32
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3.

電子ブック
ＥＢ
3. Group theory : application to the physics of condensed matter (: electronic bk)
M.S. Dresselhaus, G. Dresselhaus, A. Jorio
出版情報: [Ann Arbor, Mich.] : ProQuest Ebook Central, [20--]  1 online resource (xv, 582 p.)
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Basic Mathematics / Part I：
Basic Mathematical Background: Introduction / 1：
Definition of a Group / 1.1：
Simple Example of a Group / 1.2：
Basic Definitions / 1.3：
Rearrangement Theorem / 1.4：
Cosets / 1.5：
Conjugation and Class / 1.6：
Factor Groups / 1.7：
Group Theory and Quantum Mechanics / 1.8：
Representation Theory and Basic Theorems / 2：
Important Definitions / 2.1：
Matrices / 2.2：
Irreducible Representations / 2.3：
The Unitarity of Representations / 2.4：
Schur's Lemma (Part 1) / 2.5：
Schur's Lemma (Part 2) / 2.6：
Wonderful Orthogonality Theorem / 2.7：
Representations and Vector Spaces / 2.8：
Character of a Representation / 3：
Definition of Character / 3.1：
Characters and Class / 3.2：
Wonderful Orthogonality Theorem for Character / 3.3：
Reducible Representations / 3.4：
The Number of Irreducible Representations / 3.5：
Second Orthogonality Relation for Characters / 3.6：
Regular Representation / 3.7：
Setting up Character Tables / 3.8：
Schoenflies Symmetry Notation / 3.9：
The Hermann-Mauguin Symmetry Notation / 3.10：
Symmetry Relations and Point Group Classifications / 3.11：
Basis Functions / 4：
Symmetry Operations and Basis Functions / 4.1：
Basis Functions for Irreducible Representations / 4.2：
Projection Operators P[subscript kl superscript (Gamma subscript n)] / 4.3：
Derivation of an Explicit Expression for P[subscript kl superscript (Gamma subscript n)] / 4.4：
The Effect of Projection Operations on an Arbitrary Function / 4.5：
Linear Combinations of Atomic Orbitals for Three Equivalent Atoms at the Corners of an Equilateral Triangle / 4.6：
The Application of Group Theory to Quantum Mechanics / 4.7：
Introductory Application to Quantum Systems / Part II：
Splitting of Atomic Orbitals in a Crystal Potential / 5：
Introduction / 5.1：
Characters for the Full Rotation Group / 5.2：
Cubic Crystal Field Environment for a Paramagnetic Transition Metal Ion / 5.3：
Comments on Basis Functions / 5.4：
Comments on the Form of Crystal Fields / 5.5：
Application to Selection Rules and Direct Products / 6：
The Electromagnetic Interaction as a Perturbation / 6.1：
Orthogonality of Basis Functions / 6.2：
Direct Product of Two Groups / 6.3：
Direct Product of Two Irreducible Representations / 6.4：
Characters for the Direct Product / 6.5：
Selection Rule Concept in Group Theoretical Terms / 6.6：
Example of Selection Rules / 6.7：
Molecular Systems / Part III：
Electronic States of Molecules and Directed Valence / 7：
General Concept of Equivalence / 7.1：
Directed Valence Bonding / 7.3：
Diatomic Molecules / 7.4：
Homonuclear Diatomic Molecules / 7.4.1：
Heterogeneous Diatomic Molecules / 7.4.2：
Electronic Orbitals for Multiatomic Molecules / 7.5：
The NH[subscript 3] Molecule / 7.5.1：
The CH[subscript 4] Molecule / 7.5.2：
The Hypothetical SH[subscript 6] Molecule / 7.5.3：
The Octahedral SF[subscript 6] Molecule / 7.5.4：
[sigma]- and [pi]-Bonds / 7.6：
Jahn-Teller Effect / 7.7：
Molecular Vibrations, Infrared, and Raman Activity / 8：
Molecular Vibrations: Background / 8.1：
Application of Group Theory to Molecular Vibrations / 8.2：
Finding the Vibrational Normal Modes / 8.3：
Molecular Vibrations in H[subscript 2]O / 8.4：
Overtones and Combination Modes / 8.5：
Infrared Activity / 8.6：
Raman Effect / 8.7：
Vibrations for Specific Molecules / 8.8：
The Linear Molecules / 8.8.1：
Vibrations of the NH[subscript 3] Molecule / 8.8.2：
Vibrations of the CH[subscript 4] Molecule / 8.8.3：
Rotational Energy Levels / 8.9：
The Rigid Rotator / 8.9.1：
Wigner-Eckart Theorem / 8.9.2：
Vibrational-Rotational Interaction / 8.9.3：
Application to Periodic Lattices / Part IV：
Space Groups in Real Space / 9：
Mathematical Background for Space Groups / 9.1：
Space Groups Symmetry Operations / 9.1.1：
Compound Space Group Operations / 9.1.2：
Translation Subgroup / 9.1.3：
Symmorphic and Nonsymmorphic Space Groups / 9.1.4：
Bravais Lattices and Space Groups / 9.2：
Examples of Symmorphic Space Groups / 9.2.1：
Cubic Space Groups and the Equivalence Transformation / 9.2.2：
Examples of Nonsymmorphic Space Groups / 9.2.3：
Two-Dimensional Space Groups / 9.3：
2D Oblique Space Groups / 9.3.1：
2D Rectangular Space Groups / 9.3.2：
2D Square Space Group / 9.3.3：
2D Hexagonal Space Groups / 9.3.4：
Line Groups / 9.4：
The Determination of Crystal Structure and Space Group / 9.5：
Determination of the Crystal Structure / 9.5.1：
Determination of the Space Group / 9.5.2：
Space Groups in Reciprocal Space and Representations / 10：
Reciprocal Space / 10.1：
Representations for the Translation Group / 10.2：
Bloch's Theorem and the Basis of the Translational Group / 10.2.2：
Symmetry of k Vectors and the Group of the Wave Vector / 10.3：
Point Group Operation in r-space and k-space / 10.3.1：
The Group of the Wave Vector G[subscript k] and the Star of k / 10.3.2：
Effect of Translations and Point Group Operations on Bloch Functions / 10.3.3：
Space Group Representations / 10.4：
Symmorphic Group Representations / 10.4.1：
Nonsymmorphic Group Representations and the Multiplier Algebra / 10.4.2：
Characters for the Equivalence Representation / 10.5：
Common Cubic Lattices: Symmorphic Space Groups / 10.6：
The [Gamma] Point / 10.6.1：
Points with k [not equal] 0 / 10.6.2：
Compatibility Relations / 10.7：
The Diamond Structure: Nonsymmorphic Space Group / 10.8：
Factor Group and the [Gamma] Point / 10.8.1：
Finding Character Tables for all Groups of the Wave Vector / 10.8.2：
Electron and Phonon Dispersion Relation / Part V：
Applications to Lattice Vibrations / 11：
Lattice Modes and Molecular Vibrations / 11.1：
Zone Center Phonon Modes / 11.3：
The NaCl Structure / 11.3.1：
The Perovskite Structure / 11.3.2：
Phonons in the Nonsymmorphic Diamond Lattice / 11.3.3：
Phonons in the Zinc Blende Structure / 11.3.4：
Lattice Modes Away from k = 0 / 11.4：
Phonons in NaCl at the X Point k = ([pi]/a)(100) / 11.4.1：
Phonons in BaTiO[subscript 3] at the X Point / 11.4.2：
Phonons at the K Point in Two-Dimensional Graphite / 11.4.3：
Phonons in Te and [alpha]-Quartz Nonsymmorphic Structures / 11.5：
Phonons in Tellurium / 11.5.1：
Phonons in the [alpha]-Quartz Structure / 11.5.2：
Effect of Axial Stress on Phonons / 11.6：
Electronic Energy Levels in a Cubic Crystals / 12：
Plane Wave Solutions at k = 0 / 12.1：
Symmetrized Plane Solution Waves along the [Delta]-Axis / 12.3：
Plane Wave Solutions at the X Point / 12.4：
Effect of Glide Planes and Screw Axes / 12.5：
Energy Band Models Based on Symmetry / 13：
k [middle dot] p Perturbation Theory / 13.1：
Example of k [middle dot] p Perturbation Theory for a Nondegenerate [characters not reproducible] Band / 13.3：
Two Band Model: Degenerate First-Order Perturbation Theory / 13.4：
Degenerate second-order k [middle dot] p Perturbation Theory / 13.5：
Nondegenerate k [middle dot] p Perturbation Theory at a [Delta] Point / 13.6：
Use of k [middle dot] p Perturbation Theory to Interpret Optical Experiments / 13.7：
Application of Group Theory to Valley-Orbit Interactions in Semiconductors / 13.8：
Background / 13.8.1：
Impurities in Multivalley Semiconductors / 13.8.2：
The Valley-Orbit Interaction / 13.8.3：
Spin-Orbit Interaction in Solids and Double Groups / 14：
Crystal Double Groups / 14.1：
Double Group Properties / 14.3：
Crystal Field Splitting Including Spin-Orbit Coupling / 14.4：
Basis Functions for Double Group Representations / 14.5：
Some Explicit Basis Functions / 14.6：
Basis Functions for Other [Gamma subscript 8 superscript +] States / 14.7：
Comments on Double Group Character Tables / 14.8：
Plane Wave Basis Functions for Double Group Representations / 14.9：
Group of the Wave Vector for Nonsymmorphic Double Groups / 14.10：
Application of Double Groups to Energy Bands with Spin / 15：
E(k) for the Empty Lattice Including Spin-Orbit Interaction / 15.1：
The k [middle dot] p Perturbation with Spin-Orbit Interaction / 15.3：
E(k) for a Nondegenerate Band Including Spin-Orbit Interaction / 15.4：
E(k) for Degenerate Bands Including Spin-Orbit Interaction / 15.5：
Effective g-Factor / 15.6：
Fourier Expansion of Energy Bands: Slater-Koster Method / 15.7：
Contributions at d = 0 / 15.7.1：
Contributions at d = 1 / 15.7.2：
Contributions at d = 2 / 15.7.3：
Summing Contributions through d = 2 / 15.7.4：
Other Degenerate Levels / 15.7.5：
Other Symmetries / Part VI：
Time Reversal Symmetry / 16：
The Time Reversal Operator / 16.1：
Properties of the Time Reversal Operator / 16.2：
The Effect of T on E(k), Neglecting Spin / 16.3：
The Effect of T on E(k), Including the Spin-Orbit Interaction / 16.4：
Magnetic Groups / 16.5：
Types of Elements / 16.5.1：
Types of Magnetic Point Groups / 16.5.3：
Properties of the 58 Magnetic Point Groups {A[subscript i], M[subscript k]} / 16.5.4：
Examples of Magnetic Structures / 16.5.5：
Effect of Symmetry on the Spin Hamiltonian for the 32 Ordinary Point Groups / 16.5.6：
Permutation Groups and Many-Electron States / 17：
Classes and Irreducible Representations of Permutation Groups / 17.1：
Basis Functions of Permutation Groups / 17.3：
Pauli Principle in Atomic Spectra / 17.4：
Two-Electron States / 17.4.1：
Three-Electron States / 17.4.2：
Four-Electron States / 17.4.3：
Five-Electron States / 17.4.4：
General Comments on Many-Electron States / 17.4.5：
Symmetry Properties of Tensors / 18：
Independent Components of Tensors Under Permutation Group Symmetry / 18.1：
Independent Components of Tensors: Point Symmetry Groups / 18.3：
Independent Components of Tensors Under Full Rotational Symmetry / 18.4：
Tensors in Nonlinear Optics / 18.5：
Cubic Symmetry: O[subscript h] / 18.5.1：
Tetrahedral Symmetry: T[subscript d] / 18.5.2：
Hexagonal Symmetry: D[subscript 6h] / 18.5.3：
Elastic Modulus Tensor / 18.6：
Full Rotational Symmetry: 3D Isotropy / 18.6.1：
Icosahedral Symmetry / 18.6.2：
Cubic Symmetry / 18.6.3：
Other Symmetry Groups / 18.6.4：
Point Group Character Tables / A：
Tables for 3D Space Groups / B：
Real Space / C.1：
Tables for Double Groups / C.2：
Group Theory Aspects of Carbon Nanotubes / E：
Nanotube Geometry and the (n, m) Indices / E.1：
Lattice Vectors in Real Space / E.2：
Lattice Vectors in Reciprocal Space / E.3：
Compound Operations and Tube Helicity / E.4：
Character Tables for Carbon Nanotubes / E.5：
Permutation Group Character Tables / F：
References
Index
Basic Mathematics / Part I：
Basic Mathematical Background: Introduction / 1：
Definition of a Group / 1.1：
4.

図書
図書
4. Sketches of an elephant : a topos theory compendium (v. 1 ; v. 2 ; : set)
Peter T. Johnstone
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, c2002  2 v. ; 24 cm
シリーズ名: Oxford logic guides ; 43-44
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Regular and Cartesian Closed Categories / A1：
Toposes - Basic Theory / A2：
Allegories / A3：
Geometric Morphisms - Basic Theory / A4：
Fibrations and Indexed Categories / B1：
Internal and Locally Internal Categories / B2：
Toposes over a base / B3：
BTop/S as a 2-Category / B4：
Regular and Cartesian Closed Categories / A1：
Toposes - Basic Theory / A2：
Allegories / A3：
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