| Title:
|
Odd order semidirect extensions of commutative automorphic loops (English) |
| Author:
|
Jedlička, Přemysl |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
447-456 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We analyze semidirect extensions of middle nuclei of commutative automorphic loops. We find a less complicated conditions for the semidirect construction when the middle nucleus is an odd order abelian group. We then use the description to study extensions of orders $3$ and $5$. (English) |
| Keyword:
|
automorphic loop |
| Keyword:
|
semidirect product |
| Keyword:
|
middle nucleus |
| Keyword:
|
cyclic group |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06391553 |
| idMR:
|
MR3269007 |
| . |
| Date available:
|
2014-10-09T09:46:22Z |
| Last updated:
|
2017-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143969 |
| . |
| Reference:
|
[1] 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:
|
[2] Hora J., Jedlička P.: Nuclear semidirect product of commutative automorphic loops.J. Algebra Appl. 13 (2014), no. 1. Zbl 1292.20072, MR 3096858, 10.1142/S0219498813500771 |
| Reference:
|
[3] Jedlička P., Kinyon M., Vojtěchovský P.: 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:
|
[4] 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:
|
[5] Jedlička P., Simon D.: On commutative A-loops of order $pq$.to appear. |
| Reference:
|
[6] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Heldermann, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| . |
