Groups and symmetry

M.A. Armstrong

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.

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  • 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.

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書名 Groups and symmetry
著作者等 Armstrong, M. A.
Armstrong Mark A.
シリーズ名 Undergraduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1988
版表示 1st ed. 1988. Corr. 2nd printing 1997
ページ数 xi, 186 p.
大きさ 25 cm
ISBN 0387966757
NCID BA04835754
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言語 英語
出版国 アメリカ合衆国