| Title:
|
On Mikheev's construction of enveloping groups (English) |
| Author:
|
Hall, J. I. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
245-252 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Mikheev, starting from a Moufang loop, constructed a groupoid and reported that this groupoid is in fact a group which, in an appropriate sense, is universal with respect to enveloping the Moufang loop. Later Grishkov and Zavarnitsine gave a complete proof of Mikheev's results. Here we give a direct and self-contained proof that Mikheev's groupoid is a group, in the process extending the result from Moufang loops to Bol loops. (English) |
| Keyword:
|
Bol loop |
| Keyword:
|
Moufang loop |
| Keyword:
|
autotopism group |
| Keyword:
|
group with triality |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20059 |
| idMR:
|
MR2682477 |
| . |
| Date available:
|
2010-05-21T12:46:50Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140103 |
| . |
| Reference:
|
[1] Bruck R.H.: A Survey of Binary Systems.Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 20, Springer, Berlin-Göttingen-Heidelberg, 1958. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[2] Doro S.: Simple Moufang loops.Math. Proc. Cambridge Philos. Soc. 83 (1978), 377–392. Zbl 0381.20054, MR 0492031, 10.1017/S0305004100054669 |
| Reference:
|
[3] Grishkov A.N., Zavarnitsine A.V.: Groups with triality.J. Algebra Appl. 5 (2006), 441–463. Zbl 1110.20023, MR 2239539, 10.1142/S021949880600182X |
| Reference:
|
[4] Hall J.I.: Moufang loops and groups with triality are essentially the same thing.submitted. |
| Reference:
|
[5] Mikheev P.O.: Enveloping groups of Moufang loops.Uspekhi Mat. Nauk 48 (1993), 191–192; translation in Russian Math. Surveys 48 (1993), 195–196. Zbl 0806.20059, MR 1239875 |
| Reference:
|
[6] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Sigma Series in Pure Mathematics, 7, Heldermann, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| . |
