| Title:
|
Powers of elements in Jordan loops (English) |
| Author:
|
Pula, Kyle |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
291-299 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A Jordan loop is a commutative loop satisfying the Jordan identity $(x^2 y)x = x^2(y x)$. We establish several identities involving powers in Jordan loops and show that there is no nonassociative Jordan loop of order $9$. (English) |
| Keyword:
|
Jordan loop |
| Keyword:
|
Jordan quasigroup |
| Keyword:
|
well-defined powers |
| Keyword:
|
nonassociative loop |
| Keyword:
|
order of a loop |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1192.20060 |
| idMR:
|
MR2426893 |
| . |
| Date available:
|
2009-05-05T17:11:23Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119723 |
| . |
| Reference:
|
[1] Bruck R.H.: A Survey of Binary Systems.Ergebnisse der Mathematik und Ihrer Grenzgebiete, New Series, Vol. 20, Springer, Berlin, 1958. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[2] Goodaire E.G., Keeping R.G.: Jordan loops and loop rings.preprint. MR 2376868 |
| Reference:
|
[3] Kinyon M.K., Pula J.K., Vojtěchovský P.: Admissible Orders of Jordan Loops.J. Combinatorial Designs, to appear. |
| Reference:
|
[4] McCrimmon K.: A Taste of Jordan Algebras.Universitext, Springer, New York, 2004. Zbl 1044.17001, MR 2014924 |
| Reference:
|
[5] McCune W.W.: Mace4 Reference Manual and Guide.Tech. Memo ANL/MCS-TM-264, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, August 2003; {http://www.cs.unm.edu/$^{\sim}$mccune/mace4/}. |
| Reference:
|
[6] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Sigma Series in Pure Mathematics 7, Heldermann Verlag, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| . |
