Format:
1 online resource (328 pages)
ISBN:
9781614442110
Series Statement:
Dolciani Mathematical Expositions v.48
Content:
Intro -- copyright page -- title page -- Contents -- Preface -- A Guide to this Guide -- Algebra: Classical, Modern, and Ultramodern -- The Beginnings of Modern Algebra -- Modern Algebra -- Ultramodern Algebra -- What Next? -- Categories -- Categories -- Functors -- Natural Transformations -- Products, Coproducts, and Generalizations -- Algebraic Structures -- Structures with One Operation -- Rings -- Actions -- Semirings -- Algebras -- Ordered Structures -- Groups and their Representations -- Definitions -- Groups and homomorphisms -- Subgroups -- Actions -- G acting on itself -- Some Important Examples -- Permutation groups -- Symmetry groups -- Other examples -- Topological groups -- Free groups -- Reframing the Definitions -- Orbits and Stabilizers -- Stabilizers -- Orbits -- Acting by multiplication -- Cosets -- Counting cosets and elements -- Double cosets -- A nice example -- Homomorphisms and Subgroups -- Kernel, image, quotient -- Homomorphism theorems -- Exact sequences -- Hölder's dream -- Many Cheerful Subgroups -- Generators, cyclic groups -- Elements of finite order -- Finitely generated groups and the Burnside problem -- Other nice subgroups -- Conjugation and the class equation -- p-groups -- Sylow's Theorem and Sylow subgroups -- Sequences of Subgroups -- Composition series -- Central series, derived series, nilpotent, solvable -- New Groups from Old -- Direct products -- Semidirect products -- Isometries of R3 -- Free products -- Direct sums of abelian groups -- Inverse limits and direct limits -- Generators and Relations -- Definition and examples -- Cayley graphs -- The word problem -- Abelian Groups -- Torsion -- The structure theorem -- Small Groups -- Order four, order p2 -- Order six, order pq -- Order eight, order p3 -- And so on -- Groups of Permutations -- Cycle notation and cycle structure.
Note:
Description based on publisher supplied metadata and other sources
Additional Edition:
9780883853559
Additional Edition:
Erscheint auch als Druck-Ausgabe Gouvêa, Fernando Q., 1957 - A guide to groups, rings, and fields [Washington, DC] : Math. Ass. of America, 2012 0883853558
Additional Edition:
9780883853559
Additional Edition:
9781614442110
Language:
English
Subjects:
Mathematics
Keywords:
Algebraische Gruppe
;
Ring
;
Feld
URL:
Volltext
(lizenzpflichtig)
