| Title:
|
Moufang loops of order 243 (English) |
| Author:
|
Slattery, Michael C. |
| Author:
|
Zenisek, Ashley L. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
423-428 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed. (English) |
| Keyword:
|
Moufang |
| Keyword:
|
finite loops |
| Keyword:
|
classification of Moufang loops |
| Keyword:
|
GAP |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1256.20064 |
| idMR:
|
MR3017840 |
| . |
| Date available:
|
2012-08-31T11:40:42Z |
| Last updated:
|
2014-10-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142934 |
| . |
| Reference:
|
[1] Chee W.L.: Classification of Moufang loops of odd order.PhD thesis, Universiti Sains Malaysia, 2010. |
| Reference:
|
[2] Chein O.: Moufang loops of small order $1$.Trans. Amer. Math. Soc. 188 (1974), 31–51. MR 0330336, 10.1090/S0002-9947-1974-0330336-3 |
| Reference:
|
[3] Chein O., Pflugfelder H.O.: The smallest Moufang loop.Arch. Math. (Basel) 22 (1971), 573–576. Zbl 0241.20061, MR 0297914, 10.1007/BF01222620 |
| Reference:
|
[4] Chein O., Pflugfelder H.O.: Moufang loops of small order.Mem. Amer. Math. Soc. 13 (1978), 1–131. MR 0466391 |
| Reference:
|
[5] The GAP Group: GAP – Groups, Algorithms, and Programming, Version $4.4.12$.(2008), \verb+(http://www.gap-system.org)+. |
| Reference:
|
[6] Nagy G., Valsecchi M.: On nilpotent Moufang loops with central associators.J. Algebra 307 (2007), 547–564. Zbl 1117.20050, MR 2275362, 10.1016/j.jalgebra.2006.01.031 |
| Reference:
|
[7] Nagy G., Vojtěchovský P.: LOOPS: Computing with quasigroups and loops in GAP, Version $2.0.0$.(2008), \verb+(http://www.math.du.edu/loops)+. |
| Reference:
|
[8] Nagy G., Vojtěchovský P.: The Moufang loops of order $64$ and $81$.J. Symbolic Comput. 42 (2007), 871–883. Zbl 1131.20053, MR 2355056, 10.1016/j.jsc.2007.06.004 |
| . |
