The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.
Topics in Group Theory
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Inside This Book
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First Sentence:
In this chapter we recap basic definitions and results from the theory of groups, up to and including Lagrange's Theorem. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
how many essentially different ways, colouring polynomial, generating rank, third isomorphism theorem, elementary transpositions, internal direct product, generated nilpotent group, left transversal, right transversal, first isomorphism theorem, subnormal series, trivial group, second isomorphism theorem, rigid symmetries, infinite cyclic group, finitely generated abelian group, finite simple groups, symmetric closure, central series, maximal subgroup, cycle shape, wreath product, finite presentation, nilpotent groups, proper subgroup Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Suppose, Von Dyck, Proof Let, Proof Topics, Proof Choose, Proof First, Zassenhaus's Butterfly Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we recap basic definitions and results from the theory of groups, up to and including Lagrange's Theorem. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
how many essentially different ways, colouring polynomial, generating rank, third isomorphism theorem, elementary transpositions, internal direct product, generated nilpotent group, left transversal, right transversal, first isomorphism theorem, subnormal series, trivial group, second isomorphism theorem, rigid symmetries, infinite cyclic group, finitely generated abelian group, finite simple groups, symmetric closure, central series, maximal subgroup, cycle shape, wreath product, finite presentation, nilpotent groups, proper subgroup Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Suppose, Von Dyck, Proof Let, Proof Topics, Proof Choose, Proof First, Zassenhaus's Butterfly Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 43
books:
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24
books
cite this book:
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- Topics in Algebra by I. N. Herstein in Front Matter, and Back Matter
- Groups, Rings and Fields (Springer Undergraduate Mathematics Series) by David A.R. Wallace in Front Matter (1), and Front Matter (2)
- A Course in the Theory of Groups (Graduate Texts in Mathematics) by Derek J.S. Robinson in Front Matter, and Back Matter
- Elementary Differential Geometry by A.N. Pressley in Front Matter
- A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series) by Ian Anderson in Front Matter
See all 43 books this book cites
- Symmetries (Springer Undergraduate Mathematics Series) by D.L. Johnson in Front Matter, and Back Matter
- A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series) by Ian Anderson in Front Matter
- Real Analysis by John M. Howie in Front Matter
- Elementary Differential Geometry by A.N. Pressley in Front Matter
- Probability Models by John Haigh in Front Matter
See all 24 books citing this book
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