| Title:
|
On affine planes non-extensible to Laguerre planes and some related problems (English) |
| Author:
|
Gozdalska, Krystyna |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
2-11 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some examples of affine planes non-extensible to a Laguerre plane are studied and conditions for the uniqueness of a Laguerre extension are given. (English) |
| Keyword:
|
Laguerrian extensions |
| Keyword:
|
the Hughes projective plane over nearfield |
| MSC:
|
51B15 |
| idZBL:
|
Zbl 0721.51006 |
| idMR:
|
MR1100422 |
| DOI:
|
10.21136/MB.1991.126197 |
| . |
| Date available:
|
2009-09-24T20:42:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126197 |
| . |
| Reference:
|
[1] R. Artzy: A symmetry theorem for Laguerre planes.Journal of Geometry, 5(2) (1974), 1-8. Zbl 0287.50018, MR 0380621, 10.1007/BF01949677 |
| Reference:
|
[2] Yi Chen: A characterization of some geometries of chains.Can. J. Math., No. 2, 26 (1974), 258-260. Zbl 0281.50011, MR 0338919 |
| Reference:
|
[3] K. Gozdalska: Zagadnienie rozszerzalności afinicznych struktur incydencyjnych do płaszczyzn Laguerre'a.doctor thesis, Toruń 1985. |
| Reference:
|
[4] K. Gozdalska: Affine planes which induce Laguerre planes.Geometria, Scient. Chapt. of Institute of Technology in Poznań, 15 (1986), 99-110. Zbl 0605.51006, MR 0865126 |
| Reference:
|
[5] E. Hartman: Еine Klasse nicht einbettbarer reeller Laguerre-Еbenen.Journal of Geometry, 13(1) (1979), 49-67. MR 0547163, 10.1007/BF01988555 |
| Reference:
|
[6] E. Hartman: Moulton-Laguerre-Еbenen.Arch. Math., 17 (1976), 424-435. MR 0420431 |
| Reference:
|
[7] D. R. Hughes: A class of non-Desarguesian projective planes.Can. J. Math., No. 3, 9 (1957), 378-388. Zbl 0082.35701, MR 0087960 |
| Reference:
|
[8] J. Hunjic M. Polonijo V. Volenec: Uniqueness of the сompletion of the Еuсlidean plane to a Möbius plane.Glasnik Matematiсki, No. 1, 9 (29) (1974), 125-130. MR 0348625 |
| . |
