Main Classes Of Groups Including Permutation Groups, Matrix Groups, Transformation Groups, Abstract Groups, And Topological An

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group... Read more

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra. Various physical systems, such as crystals and the hydrogen atom, can be modelled by symmetry groups. The range of groups being considered has gradually expanded from finite permutation groups and special examples of matrix groups to abstract groups that may be specified through a presentation by generators and relations. This book studies main classes of groups including bijection, inversion, classical groups, linear maps, and algebraic variety. Project Webster represents a new publishing paradigm, allowing disparate content sources to be curated into cohesive, relevant, and informative books. To date, this content has been curated from Wikipedia articles and images under Creative Commons licensing, although as Project Webster continues to increase in scope and dimension, more licensed and public domain content is being added. We believe books such as this represent a new and exciting lexicon in the sharing of human knowledge. Less