Finite Collineation Groups: With An Introduction To The Theory Of Groups Of Operators And Substitution Groups (1917)

Finite Collineation Groups: With An Introduction To The Theory Of Groups Of Operators And Substitution Groups is a book written by Hans Frederik Blichfeldt and first published in 1917. The book is a comprehensive study of finite collineation groups, which are groups of transformations that preserve collinearity (the property of lying on a straight line) in a given geometry. The book begins with an introduction to the basic concepts of group theory, including group operations, subgroups, and homomorphisms. It then moves on to discuss collineation groups, including their definition, properties, and classification. Blichfeldt provides numerous examples of collineation groups and their applications in geometry and algebra.The second part of the book is devoted to the theory of groups of operators, which are groups of transformations that preserve a given set of operations. Blichfeldt discusses the basic properties of these groups, including their structure and classification, and provides examples of their use in geometry and algebra.The final part of the book is dedicated to substitution groups, which are groups of permutations that preserve a given set of relations. Blichfeldt provides a detailed discussion of the basic properties of these groups, including their structure and classification, and provides examples of their use in algebra and number theory.Overall, Finite Collineation Groups: With An Introduction To The Theory Of Groups Of Operators And Substitution Groups is a comprehensive and authoritative text on the theory of finite collineation groups, and is an essential reference for anyone interested in the study of group theory, geometry, and algebra.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.