Geometry and Collineation Groups of the Finite Projective Plane Pg(2, 2²) (Classic Reprint): A Dissertation - Softcover
Synopsis
Explore the mathematics of symmetry in a finite world. This work delivers a rigorous look at how collineations act on a finite projective plane and what that means for geometry and groups.
This dissertation examines PG(2, 2^2), the finite projective plane, and the transformations that preserve its structure. It highlights how conics behave, how tangents are characterized, and how group actions reveal the plane’s deep symmetries. Read as a careful study in abstract geometry, it ties together definitions, theorems, and concrete computations to map the landscape of finite geometry.
- Foundations of finite projective planes and the role of lines, points, and duality.
- Definitions and properties of conics and tangents within PG(2, 2^2).
- Detailed analysis of collineation groups, including the Hessian group and its subgroups.
- Connections between algebraic structures and geometric configurations in a rigorous setting.
Ideal for readers of advanced geometry and algebra who want a precise, worked look at finite planes and their symmetries.
"synopsis" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for Geometry and Collineation Groups of the Finite Projective...
Seller Image
Geometry and Collineation Groups of the Finite Projective Plane Pg(2, 2Â )
Print on DemandSeller: Forgotten Books, London, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: New. 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. print-on-demand item. Seller Inventory # 9781333347659_0
Buy New
US$ 17.55
Free Shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: Over 20 available
Stock Image
Geometry and Collineation Groups of the Finite Projective Plane Pg2, 2 A Dissertation Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333347659
Stock Image
Geometry and Collineation Groups of the Finite Projective Plane Pg2, 2 A Dissertation Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 4 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333347659
Buy New
US$ 24.30
US$ 4.45 shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: 15 available