Geometry and Collineation Groups of the Finite Projective Plane Pg(2, 2Â )
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
£ 13.64
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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
- Title
- Geometry and Collineation Groups of the Finite Projective Plane Pg(2, 2Â )
- Author
- Ulysses Grant Mitchell
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1333347650
- ISBN 13
- 9781333347659
- Seller catalogs
- Geometry
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.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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