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Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.

Abelian groups --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Commutative groups --- Group theory

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This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essent

Link theory. --- Invariants. --- Abelian groups. --- Commutative groups --- Group theory --- Low-dimensional topology --- Piecewise linear topology

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Infinite Abelian Groups, Volume 1

Abelian groups. --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Commutative groups --- Group theory --- Abelian groups --- Groupes (algebre) --- Groupes abeliens

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Group theory --- 51 --- Abelian groups --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Commutative groups --- Mathematics --- Abelian groups. --- Modules (Algebra). --- 51 Mathematics

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512.54 --- Abelian groups --- Commutative groups --- Group theory --- Groups. Group theory --- Abelian groups. --- 512.54 Groups. Group theory --- Groupes (algebre) --- Groupes abeliens