1 edition of An introduction to the theory of groups found in the catalog.
An introduction to the theory of groups
P. S. Aleksandrov
Translation of Einführung in die Gruppentheorie.
|Statement||P.S. Alexandroff ; translated by Hazel Perfect and G. M. Petersen|
|LC Classifications||QA 171 A36 E3 E|
|The Physical Object|
|Number of Pages||112|
Group theory is the study of groups. Groups are sets equipped with an operation (like multiplication, addition, or composition) that satisfies certain basic properties. As the building blocks of abstract algebra, groups are so general and fundamental that they arise in nearly every branch of mathematics and the sciences. For example: Symmetry groups appear in the study . An Introduction to Group Theory in particular) and in Mathematics itself. Group Theory extracts the essential characteristics of diverse situations in which some type of symmetry or transformation appears. Given a non-empty set, a binary operation is defined on it such that certain axioms hold, that is, it possesses a structure (the group /5(15).
This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates, developing material of fundamental importance in a clear and rigorous fashion. A wealth of simple examples, primarily geometrical, illustrate the primary concepts. Exercises at the end of each chapter provide additional reinforcement. edition. Theory, Solvable groups, Jordan-Holder Theorem, P. Hall's Theorem on solvable groups of order ab, where (a, b) = 1, Nilpotent groups; 7: Automorphism groups, Extensions, Second Cohomology group; 8: Finite fields, Simplicity of the projective unimodular groups PSL(m, K) when m > 3 or when m = 2 and K is a finite field of. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students.
Part of the Graduate Texts in Mathematics book series (GTM, volume ) Log in to check access Permutations and the Mathieu Groups. Joseph J. Rotman. Pages Abelian Groups About this book. Keywords. Abelian group Abstract algebra Galois theory algebra automorphism cohomology commutative ring semigroup. Authors and affiliations. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as. Introduction to Group Theory. Groups where * is commutative are called abelian groups My college courses in abstract algebra were based on the book A Book of Abstract Algebra by Charles.
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SyntaxTextGen not activatedAdditional Physical Format: Online version: Aleksandrov, P.S. (Pavel Sergeevich), Introduction to the theory of groups. New York: Hafner, .theory of nite groups.
The goal of this book is to give a \holistic" introduction to rep-resentation theory, presenting it as a uni ed subject which studies representations of associative algebras and treating the representa-tion theories of groups, Lie algebras, and quivers as special cases.
ItFile Size: KB.An introduction to ebook theory of groups. [Joseph J Rotman] Home. WorldCat Home About WorldCat Help. Search. Search ebook Library Items Search for Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book.
The first six chapters provide material for a first course, while the rest of the book covers.