| Title:
|
A-loops close to code loops are groups (English) |
| Author:
|
Drápal, Aleš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
245-249 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $Q$ be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group. (English) |
| Keyword:
|
A-loop |
| Keyword:
|
central nilpotency |
| Keyword:
|
Osborn problem |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1038.20046 |
| idMR:
|
MR1780868 |
| . |
| Date available:
|
2009-01-08T19:00:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119160 |
| . |
| Reference:
|
[1] Aschbacher M.: Sporadic Groups.Cambridge Tracts in Mathematics 104, Cambridge University Press, 1994. Zbl 0804.20011, MR 1269103 |
| Reference:
|
[2] Bruck R.H.: Contributions to the theory of loops.Trans. Amer. Math. Soc. 60 (1946), 245-354. Zbl 0061.02201, MR 0017288 |
| Reference:
|
[3] Bruck R.H., Paige L.J.: Loops whose inner mappings are automorphisms.Ann. of Math. 63 (1954), 308-323. MR 0076779 |
| Reference:
|
[4] Chein O., Goodaire E.G.: Moufang loops with a unique non-identity commutator (associator, square).J. Algebra 130 (1990), 369-384. MR 1051308 |
| Reference:
|
[5] Griess R.L., Jr.: Code loops.J. Algebra 100 (1986), 224-234. Zbl 0589.20051, MR 0839580 |
| Reference:
|
[6] Osborn M.J.: A theorem on A-loops.Proc. Amer. Math. Soc. 9 (1958), 347-349. Zbl 0097.25302, MR 0093555 |
| Reference:
|
[7] Phillips J.D.: On Moufang A-loops.Comment. Math. Univ. Carolinae 41 (2000), 371-375. Zbl 1038.20050, MR 1780878 |
| . |
