Geometry and Collineation Groups of the Finite Projective Plane Pg(2, 2Â )

Ulysses Grant Mitchell

ISBN 10: 1333347650 / ISBN 13: 9781333347659

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book offers a groundbreaking exploration of the finite projective plane PG(2,22), revealing its intriguing geometric and algebraic properties. The author, a renowned mathematician, introduces a novel approach to understanding this fascinating subject, providing a comprehensive framework for studying its symmetries and underlying structures. The book begins by defining PG(2,22) and establishing its fundamental properties, laying the groundwork for further exploration. It then delves into the classification of collineations, the transformations that preserve the geometry of the plane. The author introduces various types of collineations, including hyperbolic, parabolic, and elliptic transformations, and establishes their significance within the context of PG(2,22). Delving deeper, the author examines cyclic groups of collineations, which play a crucial role in understanding the symmetries of the plane. Through detailed analysis, the book reveals the existence of cyclic subgroups of different orders and their relationship to the overall structure of PG(2,22). The book also investigates the concept of invariant figures, geometric configurations that remain unaltered under certain transformations. The author demonstrates how the identification of invariant figures provides valuable insights into the behavior of collineations and the symmetries of the plane. The book culminates in a discussion of the group of determinant unity G20,60, the maximal simple subgroup of all collineations in PG(2,22). The author demonstrates that G20,60 possesses remarkable properties, including the ability to be generated by a collection of elations, the simplest type of transformation in the plane. This discovery underscores the fundamental role of elations in the geometry of PG(2,22). Through its rigorous analysis and insightful exploration, this book offers a profound understanding of the finite projective plane PG(2,22). It provides a valuable resource for mathematicians, geometers, and anyone fascinated by the intricate interplay of geometry and algebra. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781333347659_0

Bibliographic Details

• Title: Geometry and Collineation Groups of the Finite Projective Plane Pg(2, 2Â )
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1333347650
• ISBN 13: 9781333347659
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Geometry

About this title

Synopsis

This book offers a groundbreaking exploration of the finite projective plane PG(2,22), revealing its intriguing geometric and algebraic properties. The author, a renowned mathematician, introduces a novel approach to understanding this fascinating subject, providing a comprehensive framework for studying its symmetries and underlying structures. The book begins by defining PG(2,22) and establishing its fundamental properties, laying the groundwork for further exploration. It then delves into the classification of collineations, the transformations that preserve the geometry of the plane. The author introduces various types of collineations, including hyperbolic, parabolic, and elliptic transformations, and establishes their significance within the context of PG(2,22). Delving deeper, the author examines cyclic groups of collineations, which play a crucial role in understanding the symmetries of the plane. Through detailed analysis, the book reveals the existence of cyclic subgroups of different orders and their relationship to the overall structure of PG(2,22). The book also investigates the concept of invariant figures, geometric configurations that remain unaltered under certain transformations. The author demonstrates how the identification of invariant figures provides valuable insights into the behavior of collineations and the symmetries of the plane. The book culminates in a discussion of the group of determinant unity G20,60, the maximal simple subgroup of all collineations in PG(2,22). The author demonstrates that G20,60 possesses remarkable properties, including the ability to be generated by a collection of elations, the simplest type of transformation in the plane. This discovery underscores the fundamental role of elations in the geometry of PG(2,22). Through its rigorous analysis and insightful exploration, this book offers a profound understanding of the finite projective plane PG(2,22). It provides a valuable resource for mathematicians, geometers, and anyone fascinated by the intricate interplay of geometry and algebra.