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Article

Jedlička, Přemysl
On commutative loops of order $pq$ with metacyclic inner mapping group and trivial center. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 51 (2010), issue 2, pp. 253-261
MSC: 20N05 | MR 2682478 | Zbl 1211.20060
Keywords:
commutative loops; construction of loops; matrices over finite fields; quadratic extensions
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.
References:
[1] Drápal A.: A class of commutative loops with metacyclic inner mapping groups. Comment. Math. Univ. Carolin. 49,3 (2008), 357–382. MR 2490433
[2] Jedlička P., Simon D.: Commutative automorphic loops of order $pq$. preprint.
[3] Nagy G., Vojtěchovský P.: LOOPS: Computing with quasigroups and loops. version 2.1.0, package for GAP, http://www.math.du.edu/loops
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