| Title:
|
On centerless commutative automorphic loops (English) |
| Author:
|
Nagy, Gábor P. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
485-491 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this short paper, we survey the results on commutative automorphic loops and give a new construction method. Using this method, we present new classes of commutative automorphic loops of exponent $2$ with trivial center. (English) |
| Keyword:
|
commutative automorphic loop |
| Keyword:
|
Lie algebra of characteristic $2$ |
| Keyword:
|
nuclear extension |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06391556 |
| idMR:
|
MR3269010 |
| . |
| Date available:
|
2014-10-09T09:52:02Z |
| Last updated:
|
2017-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143972 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Csörgö P.: All automorphic loops of order $p^2$ for some prime $p$ are associative.J. Algebra Appl. 12 (2013), no. 6, 1350013. Zbl 1275.20071, MR 3063452, 10.1142/S0219498813500138 |
| Reference:
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[5] de Barros D.A.S., Grishkov A., Vojtěchovský P.: Commutative automorphic loops of order $p^3$.J. Algebra Appl. 11 (2012), 1250100. MR 2983192, 10.1142/S0219498812501009 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[8] 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:
|
[9] 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:
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[10] Jedlička P., Kinyon M., Vojtěchovský P.: Nilpotency in automorphic loops of prime power order.J. Algebra 350 (2012), 64–76. 10.1016/j.jalgebra.2011.09.034 |
| Reference:
|
[11] 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:
|
[12] Kinyon M., Grishkov A., Nagy G.P.: Solvability of commutative automorphic loops.Trans. Amer. Math. Soc., to appear, arXiv:1111.7138. MR 3223359 |
| Reference:
|
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| . |
