| Title:
|
The free commutative automorphic $2$-generated loop of nilpotency class $3$ (English) |
| Author:
|
Barros, Dylene Agda Souza de |
| Author:
|
Grishkov, Alexander |
| Author:
|
Vojtěchovský, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
321-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A loop is automorphic if all its inner mappings are automorphisms. We construct the free commutative automorphic $2$-generated loop of nilpotency class $3$. It has dimension $8$ over the integers. (English) |
| Keyword:
|
free commutative automorphic loop |
| Keyword:
|
automorphic loop |
| Keyword:
|
associator calculus |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1256.20065 |
| idMR:
|
MR3017833 |
| . |
| Date available:
|
2012-08-31T11:32:12Z |
| Last updated:
|
2014-10-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142926 |
| . |
| Reference:
|
[1] Barros D.: Commutative automorphic loops.PhD dissertation, University of Sao Paulo, in preparation. |
| Reference:
|
[2] Barros D., Grishkov A., Vojtěchovský P.: Commutative automorphic loops of order $p^3$.J. Algebra Appl.(to appear). |
| Reference:
|
[3] Bruck R.H.: A Survey of Binary Systems.Springer, 1971. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[4] Bruck R.H., Paige L.J.: Loops whose inner mappings are automorphisms.Ann. of Math. (2) 63 (1956), 308–323. Zbl 0074.01701, MR 0076779, 10.2307/1969612 |
| Reference:
|
[5] Csörgö P.: The multiplication group of a finite commutative automorphic loop of order of power of an odd prime $p$ is a $p$-group.J. Algebra 350 (2012), no. 1, 77–83. MR 2859876, 10.1016/j.jalgebra.2011.09.038 |
| Reference:
|
[6] Jedlička P., Kinyon M., Vojtěchovský P.: The structure of commutative automorphic loops.Trans. Amer. Math. Soc. 363 (2011), no. 1, 365–384. Zbl 1215.20060, MR 2719686, 10.1090/S0002-9947-2010-05088-3 |
| Reference:
|
[7] Jedlička P., Kinyon M., Vojtěchovský P.: Constructions of commutative automorphic loops.Comm. Algebra 38 (2010), no. 9, 3243–3267. Zbl 1209.20069, MR 2724218, 10.1080/00927870903200877 |
| Reference:
|
[8] Jedlička P., Kinyon M., Vojtěchovský P.: Nilpotency in automorphic loops of prime power order.J. Algebra 350 (2012), no. 1, 64–76. MR 2859875, 10.1016/j.jalgebra.2011.09.034 |
| Reference:
|
[9] Johnson K.W., Kinyon M.K., Nagy G.P., Vojtěchovský P.: Searching for small simple automorphic loops.LMS J. Comput. Math. 14 (2011), 200–213. Zbl 1225.20052, MR 2831230, 10.1112/S1461157010000173 |
| Reference:
|
[10] Grishkov A.N., Shestakov I.P.: Commutative Moufang loops and alternative algebras.J. Algebra 333 (2011), 1–13. Zbl 1243.20076, MR 2785933, 10.1016/j.jalgebra.2010.11.020 |
| Reference:
|
[11] Kinyon M.K., Kunen K., Phillips J.D., Vojtěchovský P.: The structure of automorphic loops.in preparation. |
| Reference:
|
[12] Wolfram Research, Inc.: Mathematica.version 8.0, Wolfram Research, Inc., Champaign, Illinois, 2010. |
| . |
