| Title:
|
On Moufang A-loops (English) |
| Author:
|
Phillips, J. D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
371-375 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In a series of papers from the 1940's and 1950's, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck's colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are Moufang ([5]). In [2] we relaunched this now over 50 year old program by examining conditions under which general --- not necessarily commutative --- diassociative A-loops are, in fact, Moufang. Here, we finish part of the program by characterizing Moufang A-loops. We also investigate simple diassociative A-loops as well as a class of centrally nilpotent diassociative A-loops. These results, {\it in toto}, reveal the distinguished positions two familiar classes of diassociative A-loops --- namely groups and commutative Moufang loops--play in the general theory. (English) |
| Keyword:
|
diassociative |
| Keyword:
|
A-loop |
| Keyword:
|
Moufang |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1038.20050 |
| idMR:
|
MR1780878 |
| . |
| Date available:
|
2009-01-08T19:02:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119170 |
| . |
| Reference:
|
[1] Bruck R.H., Paige L.J.: Loops whose inner mappings are automorphisms.Ann. of Math. 63 (2) (1956), 308-232. Zbl 0074.01701, MR 0076779 |
| Reference:
|
[2] Fuad T.S.R., Phillips J.D., Shen X.R.: On diassociative A-loops.submitted. |
| Reference:
|
[3] Glauberman G.: On loops of odd order II.J. Algebra 8 (1968), 393-414. Zbl 0155.03901, MR 0222198 |
| Reference:
|
[4] Moufang R.: Zur struktur von alternativkorpern.Math. Ann. 110 (1935), 416-430. MR 1512948 |
| Reference:
|
[5] Osborn J.M.: A theorem on A-loops.Proc. Amer. Math. Soc. 9 (1959), 347-349. MR 0093555 |
| . |
