| Title:
|
Moufang loops of order coprime to three that cyclically extend groups of dihedral type (English) |
| Author:
|
Drápal, Aleš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
453-500 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper completely solves the isomorphism problem for Moufang loops $Q = GC$ where $G\unlhd Q$ is a noncommutative group with cyclic subgroup of index two and $|Z(G)| \le 2$, $C$ is cyclic, $G\cap C = 1$, and $Q$ is finite of order coprime to three. (English) |
| Keyword:
|
dihedral group |
| Keyword:
|
Moufang loop |
| Keyword:
|
cyclic extension |
| Keyword:
|
semidirect product |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1374.20069 |
| idMR:
|
MR3583301 |
| DOI:
|
10.14712/1213-7243.2015.187 |
| . |
| Date available:
|
2017-01-09T22:14:29Z |
| Last updated:
|
2019-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145952 |
| . |
| Reference:
|
[1] Chein O.: Moufang loops of small order, I..Trans. Amer. Math. Soc. 188 (1974), 31–51. Zbl 0286.20088, MR 0330336, 10.1090/S0002-9947-1974-0330336-3 |
| Reference:
|
[2] Chein O.: Moufang loops of small order.Mem. Amer. Math. Soc. 13 (1978), no. 197. Zbl 0378.20053, MR 0466391 |
| Reference:
|
[3] Drápal A.: On extensions of Moufang loops by a cyclic factor that is coprime to three.Comm. Algebra, (in print) http://dx.doi.org/10.1080/00927872.2016.1233202. 10.1080/00927872.2016.1233202 |
| Reference:
|
[4] Gagola S.M., III: Cyclic extensions of Moufang loops induced by semi-automorphisms.J. Algebra Appl. 13 (2014), no. 4, Article ID 1350128. Zbl 1296.20028, MR 3153863, 10.1142/S0219498813501284 |
| Reference:
|
[5] Gagola S.hM., III: Describing cyclic extensions of Bol loops.Quasigroups and Related Systems 23 (2015), 31–39. Zbl 1328.20084, MR 3353111 |
| Reference:
|
[6] Goodaire E.R., May S., Raman M.: The Moufang Loops of Order Less Than 64.Nova Science Publishers, Inc., Commack, NY, 1999. Zbl 0964.20043, MR 1689624 |
| . |
