| Title:
|
On commutative loops of order $pq$ with metacyclic inner mapping group and trivial center (English) |
| Author:
|
Jedlička, Přemysl |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
253-261 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using a construction of commutative loops with metacyclic inner mapping group and trivial center described by A. Drápal, we enumerate presumably all such loops of order $pq$, for $p$ and $q$ primes. (English) |
| Keyword:
|
commutative loops |
| Keyword:
|
construction of loops |
| Keyword:
|
matrices over finite fields |
| Keyword:
|
quadratic extensions |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20060 |
| idMR:
|
MR2682478 |
| . |
| Date available:
|
2010-05-21T12:47:06Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140104 |
| . |
| Reference:
|
[1] Drápal A.: A class of commutative loops with metacyclic inner mapping groups.Comment. Math. Univ. Carolin. 49,3 (2008), 357–382. MR 2490433 |
| Reference:
|
[2] Jedlička P., Simon D.: Commutative automorphic loops of order $pq$.preprint. |
| Reference:
|
[3] Nagy G., Vojtěchovský P.: LOOPS: Computing with quasigroups and loops.version 2.1.0, package for GAP, http://www.math.du.edu/loops. |
| . |
