Ebook266 pages10 hours
Abelian Groups
By L. Fuchs
Rating: 1 out of 5 stars
1/5
()
About this ebook
Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations.
Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups.
This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.
Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups.
This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.
Related to Abelian Groups
Titles in the series (50)
Integral Equations: And Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology Rating: 2 out of 5 stars2/5The Theory of Lebesgue Measure and Integration Rating: 0 out of 5 stars0 ratingsIntroduction to Higher Algebra Rating: 0 out of 5 stars0 ratingsAbelian Groups Rating: 1 out of 5 stars1/5Axiomatics of Classical Statistical Mechanics Rating: 0 out of 5 stars0 ratingsIntroduction to Calculus Rating: 5 out of 5 stars5/5Calculus of Variations Rating: 0 out of 5 stars0 ratingsElements of Linear Space Rating: 0 out of 5 stars0 ratingsNon-Linear Differential Equations Rating: 0 out of 5 stars0 ratingsNomography Rating: 0 out of 5 stars0 ratingsThe Fundamentals of Mathematical Analysis Rating: 2 out of 5 stars2/5Linear Representations of the Lorentz Group Rating: 0 out of 5 stars0 ratingsConvergence Problems of Orthogonal Series Rating: 0 out of 5 stars0 ratingsGeneralized Analytic Functions Rating: 0 out of 5 stars0 ratingsMathematical Analysis: Functions, Limits, Series, Continued Fractions Rating: 0 out of 5 stars0 ratingsTheory of Approximation of Functions of a Real Variable Rating: 0 out of 5 stars0 ratingsAnalytical Quadrics Rating: 0 out of 5 stars0 ratingsA Course of Higher Mathematics Rating: 0 out of 5 stars0 ratingsApplied Methods of the Theory of Random Functions Rating: 0 out of 5 stars0 ratingsMathematical Techniques of Operational Research Rating: 0 out of 5 stars0 ratingsRadiative Transfer on Discrete Spaces Rating: 0 out of 5 stars0 ratingsSome Topics in Complex Analysis Rating: 0 out of 5 stars0 ratingsThe Theory of Jets in an Ideal Fluid Rating: 5 out of 5 stars5/5Lie Algebras Rating: 0 out of 5 stars0 ratingsOperational Calculus Rating: 0 out of 5 stars0 ratingsOperational Calculus Rating: 0 out of 5 stars0 ratingsVector Measures Rating: 0 out of 5 stars0 ratingsThe Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics Rating: 0 out of 5 stars0 ratingsBoundary Value Problems Rating: 4 out of 5 stars4/5Homology Theory on Algebraic Varieties Rating: 1 out of 5 stars1/5
Related ebooks
Lectures on the Calculus of Variations Rating: 0 out of 5 stars0 ratingsAnalysis on Real and Complex Manifolds Rating: 0 out of 5 stars0 ratingsCohomology and Differential Forms Rating: 5 out of 5 stars5/5An Introduction to Orthogonal Polynomials Rating: 4 out of 5 stars4/5Abelian Varieties Rating: 0 out of 5 stars0 ratingsInfinite Abelian Groups Rating: 0 out of 5 stars0 ratingsLectures on Homotopy Theory Rating: 0 out of 5 stars0 ratingsTheory of Groups of Finite Order Rating: 0 out of 5 stars0 ratingsTopoi: The Categorial Analysis of Logic Rating: 5 out of 5 stars5/5Analysis in Euclidean Space Rating: 0 out of 5 stars0 ratingsTopological Transformation Groups Rating: 3 out of 5 stars3/5Modern Methods in Topological Vector Spaces Rating: 0 out of 5 stars0 ratingsThe Elements of Non-Euclidean Geometry Rating: 3 out of 5 stars3/5Foundations of Modern Analysis Rating: 1 out of 5 stars1/5Asymptotic Expansions Rating: 3 out of 5 stars3/5Substitutional Analysis Rating: 0 out of 5 stars0 ratingsTopos Theory Rating: 0 out of 5 stars0 ratingsProperties and Operations Rating: 0 out of 5 stars0 ratingsIntroduction to Homological Algebra, 85 Rating: 4 out of 5 stars4/5Topology: Volume I Rating: 5 out of 5 stars5/5Topological Vector Spaces and Distributions Rating: 3 out of 5 stars3/5General Topology Rating: 4 out of 5 stars4/5A Course in Advanced Calculus Rating: 3 out of 5 stars3/5Uniform Distribution of Sequences Rating: 4 out of 5 stars4/5Topological Methods in Galois Representation Theory Rating: 0 out of 5 stars0 ratingsDifferential Geometry Rating: 5 out of 5 stars5/5Differential Topology: First Steps Rating: 0 out of 5 stars0 ratingsAlgebraic Theory of Numbers: Translated from the French by Allan J. Silberger Rating: 0 out of 5 stars0 ratingsSieve Methods Rating: 0 out of 5 stars0 ratingsEquivalents of the Axiom of Choice, II Rating: 0 out of 5 stars0 ratings
Mathematics For You
Algebra - The Very Basics Rating: 5 out of 5 stars5/5Basic Math Notes Rating: 5 out of 5 stars5/5Geometry For Dummies Rating: 5 out of 5 stars5/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5Calculus For Dummies Rating: 4 out of 5 stars4/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5The Elements of Euclid for the Use of Schools and Colleges (Illustrated) Rating: 0 out of 5 stars0 ratingsThe Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5Calculus Made Easy Rating: 4 out of 5 stars4/5Is God a Mathematician? Rating: 4 out of 5 stars4/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsThe Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5GED® Math Test Tutor, 2nd Edition Rating: 0 out of 5 stars0 ratingsLogicomix: An epic search for truth Rating: 4 out of 5 stars4/5Algebra I For Dummies Rating: 4 out of 5 stars4/5
Reviews for Abelian Groups
Rating: 1 out of 5 stars
1/5
1 rating0 reviews
Book preview
Abelian Groups - L. Fuchs
Enjoying the preview?
Page 1 of 1