Groups and symmetry
著者
書誌事項
Groups and symmetry
（Undergraduate texts in mathematics）
Springer, 1997 , c1988
Corrected 3rd printing
- : gw
- : us
並立書誌 全1件
-
-
Groups and symmetry / M.A. Armstrong
BA04835754
-
Groups and symmetry / M.A. Armstrong
大学図書館所蔵 件 / 全6件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Bibliography: p. [181]
Includes index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387966755
内容説明
This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.
目次
Preface. 1: Symmetries of the Tetrahedron. 2: Axioms. 3: Numbers. 4: Dihedral Groups. 5: Subgroups and Generators. 6: Permutations. 7: Isomorphisms. 8: Plato's Solids and Cayley's Theorem. 9: Matrix Groups. 10: Products. 11: Lagrange's Theorem. 12: Partitions. 13: Cauchy's Theorem. 14: Conjugacy. 15: Quotient Groups. 16: Homomorphisms. 17: Actions, Orbits, and Stabalizers. 18: Counting Orbits. 19: Finite Rotation Groups. 20: The Sylow Theorems. 21: Finitely Generated Abelian Groups. 22: Row and Column Operations. 23: Automorphisms. 24: The Euclidean Group. 25: Lattices and Point Groups. 26: Wallpaper Patterns. 27: Free Groups and Presentations. 28: Trees and the Nielsen-Schreier Theorem. Bibliography. Index.
- 巻冊次
-
: gw ISBN 9783540966753
内容説明
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises to help develop the student's intuition.
目次
Contents: Symmetries of the Tetrahedron.- Axioms.- Numbers.- Dihedral Groups.- Subgroups and Generators.- Permutations.- Isomorphisms.- Plato's Solids and Cayley's Theorem.- Matrix Groups.- Products.- Lagrange's Theorem.- Partitions.- Cauchy's Theorem.- Conjugacy.- Quotient Groups.- Homomorphisms.- Actions, Orbits, and Stabilizers.- Counting Orbits.- Finite Rotation Groups.- The Sylow Theorems.- Finitely Generated Abelian Groups.- Row and Column Operations.- Automorphisms.- The Euclidean Group.- Lattices and Point Groups.- Wallpaper Patterns.- Free Groups and Presentations.- Trees and the Nielsen-Schreier Theorem.- Bibliography.- Index.
「Nielsen BookData」 より
