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1st Edition

Geometry of Derivation, Volume III Classification of Skewfield Flocks

By Norman L. Johnson Copyright 2026

360 Pages

by Chapman & Hall

Description

Geometry of Derivation, Volume III: Classification of Skewfield Flocks is the third book in a series of books on the topic. This book continues establishing the techniques, examples, and future directions of the specifics of flock theory over skewfields. Like its predecessors, it will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and... Read more

Table of Contents

Part 1: The Classification of Flocks

1. The Classes of Flocks

2. General Theorems of Flocks

3. The Isomorphism Questions

Part 2: Multiple Replacement−Redux

4. Extension of Division Rings

5. Automorphism Groups of Division Rings

6. The Theorem of Andre’

7. Dickson Nearfield Planes

8. Ostrom’s Theorem

Part 3: Simultaneous Flock Spreads

9. Simultaneous Spreads of Type 2

Part 4: Semifields over Division Rings

10. Twisted T-Copies

11. General Skewfield Lifts to Semifields

12. Central Extensions of Degree 3, 4

13. Central Cyclic Extensions

Part 5: Lifting Skewsfields-Degree n

14. General Lifting

Part 6: Kantor-Pentilla and CJV σ − Flokki

15. Transform and CJV-Methods

16. Choices of Representation

Part 7: JPW-Hyperbolic Flocks

17. Idea of “Left-Inversion”

Part 8: Non-Linear Hyperbolic Flocks

18. Adjoining Inner Derivation Functions

19. Resolved Conical Flocks

20. The Isomorphism Questions

21. The Hyperbolic Isomorphism Question

Part 9: The Baer Flocks

22. Draxl's Theorem

23. Transposed Baer Flocks

Part 10: Anti-Isomorphic Flocks

24. The Hyperbolic Flock Square

Part 11: Elation Group Double Covers

25. The Three Spreads of a Double Cover

26. Skew-Desarguesian Spreads

27. Right Skew-Desarguesian Spreads

Part 12: Strings

28. Strings of Quasfibrations and Spreads

29. Corresponding Right “Flocks”

Part 13: Switch and Imposter Switch

30. Derivation of Flock Spreads

Part 14: Baer Groups over Skewfields

31. Point-Baer Subplanes of Planes

32. Baer Collineations in Translation Planes

33. Derived Spreads and Baer Groups

34. Deficiency One Flocks of Order p⁴

35. t_o-Interchange-Hyperbolic Spreads

36. t_o-Interchange-Conical Spreads

37. Left Inversing “Minus One”

38. Deficiency One

39. Hyperbolic Skew-Desarguesian Flocks

Part 15: Three Line Problem

40. Do Three Components define a Pseudo-Regulus?

41. Three Component-Three Point Construction

Part 16: The Flocks and Spreads

42. Anti-Isomorphic Flocks

43. Constructions-Generalized Lifted

44. 1-A Conical Spreads

45. Flocks from Lifted Types

46. The Open Types and New Directions

Author(s)

Biography

Norman L. Johnson is an Emeritus Professor (2011) at the University of Iowa where he has had ten PhD students. He received his Ph.D. at Washington State University as a student of T.G. Ostrom. He has written 580 research items including articles, books, and chapters available on Researchgate.net. Additionally, he has worked with approximately 40 coauthors and is a previous Editor for International Journal of Pure and Applied Mathematics and Note di Matematica. Dr. Johnson plays ragtime piano and enjoys studying languages and 8-ball pool.

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