"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM
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Second Edition D.J.S. Robinson A Course in the Theory of Groups "This book is an excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The fifteen chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties . . . This book is highly recommended."—ACTA SCIENTIARUM MATHEMATICARUM
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Most Helpful Customer Reviews
14 of 15 people found the following review helpful:
5.0 out of 5 stars
The only group theory book for the advanced reader.,
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This review is from: A Course in the Theory of Groups (Graduate Texts in Mathematics) (Hardcover)
This book is, I suppose, the most authoritative and comprehensive text on group theory. Text is quite succinct and self-contained, proofs are elegant and rigorous. Only few sections of the first chapter cover undergraduate group theory. Therefore I do not recommend it for the one that would prefer an introductory text rather than a serious reference text. It is also a strong self study text, the example questions are well-chosen and generally demanding. Though its name begins with `A Course...', I think it contains enough material for more than 3 courses, a semester each. It is definitely worth its value, a must for a mathematician's library.
6 of 6 people found the following review helpful:
5.0 out of 5 stars
A very good serious book,
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This review is from: A Course in the Theory of Groups (Graduate Texts in Mathematics) (Hardcover)
This book is an excellent second book after the one from J Rotman (An introduction to the theory of groups).
Self studying with the 2 books demands a lot of work but can be achieved by someone motivated. When a concept is not understood with one of the books, the explanation read in the second really help. This book is not for a beginner, but is perfect for someone with a real mathematical background. The concepts are organised as can be the mathematical courses in universities, concise, succint and demanding.
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Inside This Book
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First Sentence:
A binary operation on a set is a rule for combining two elements of the set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
locally soluble group, generated soluble groups, supersoluble groups, minimax group, polycentral ideal, abelian series, simple subnormal subgroups, finite length whose factors, fundamental commutator identities, finitely generated soluble group, locally nilpotent groups, proper nontrivial normal subgroup, system normalizers, maximal normal abelian subgroup, normalizer condition, finite soluble group, automorphism tower, standard wreath product, quasicyclic groups, algebraically closed field whose characteristic, proper quotient group, nilpotent length, permutable subgroup, transversal function, conjugation homomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Sylow's Theorem, Maschke's Theorem, Schur's Lemma, Schur-Zassenhaus Theorem, Feit-Thompson Theorem, First Isomorphism Theorem, Jordan-Hölder Theorem, Lagrange's Theorem, Representations of Groups, Classes of Groups Defined, Grushko-Neumann Theorem, The Three Subgroup Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A binary operation on a set is a rule for combining two elements of the set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
locally soluble group, generated soluble groups, supersoluble groups, minimax group, polycentral ideal, abelian series, simple subnormal subgroups, finite length whose factors, fundamental commutator identities, finitely generated soluble group, locally nilpotent groups, proper nontrivial normal subgroup, system normalizers, maximal normal abelian subgroup, normalizer condition, finite soluble group, automorphism tower, standard wreath product, quasicyclic groups, algebraically closed field whose characteristic, proper quotient group, nilpotent length, permutable subgroup, transversal function, conjugation homomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Sylow's Theorem, Maschke's Theorem, Schur's Lemma, Schur-Zassenhaus Theorem, Feit-Thompson Theorem, First Isomorphism Theorem, Jordan-Hölder Theorem, Lagrange's Theorem, Representations of Groups, Classes of Groups Defined, Grushko-Neumann Theorem, The Three Subgroup Lemma New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- Linear Representations of Finite Groups (Graduate Texts in Mathematics) (v. 42) by Jean-Pierre Serre in Front Matter, and Back Matter
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- A Course in Homological Algebra (Graduate Texts in Mathematics) by Peter J. Hilton in Front Matter, and Back Matter
See all 100 books this book cites
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter
- Differential Analysis on Complex Manifolds (Graduate Texts in Mathematics, Vol 65) by Raymond O'Neil Wells in Back Matter
- Probability Theory II (Graduate Texts in Mathematics) by M. Loeve in Back Matter
- Optima and Equilibria: An Introduction to Nonlinear Analysis (Graduate Texts in Mathematics) by Jean-Pierre Aubin in Back Matter
- Sheaf Theory (Graduate Texts in Mathematics) by Glen E. Bredon in Back Matter
See all 100 books citing this book
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