[GAP Forum] Constructing Bol loops

[Nagy Gabor]

Hi,

Right (and left) Bol loops are contained in the libraries of the LOOPS 
package:

gap> LoadPackage("loops");
─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Loading  loops 3.4.1 (The LOOPS Package: Loops and quasigroups for GAP)
by Gábor Nagy (http://www.math.u-szeged.hu/~nagyg/) and
    Petr Vojtěchovský (http://www.math.du.edu/~petr/).
Homepage: https://gap-packages.github.io/loops/
Report issues at https://github.com/gap-packages/loops/issues
─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
true
gap> DisplayLibraryInfo("right Bol");
The library contains all nonassociative right Bol loops of order less 
than 17
and all nonassociative right Bol loops of order p*q, where p>q>2 are primes.
------
Extent of the library:
    6 loops of order 8
    3 loops of order 12
    2038 loops of order 16
    (p-q)/2 loops of order p*q for primes p>q>2 such that q divides p-1
    (p-q+2)/2 loops of order p*q for primes p>q>2 such that q divides p+1
true


The constructions are rather ad hoc. See

R.P. Burn. Finite Bol loops I. Math. Proc. Cambridge Philos. Soc., 
84(3):53–66, 1978.
G.P. Nagy, Burnside problems for Moufang and Bol loops of small 
exponent, Acta Sci. Math. (Szeged). 67 (2001) 687–696.
H. Kiechle, G.P. Nagy, On the extension of involutorial Bol loops, Abh. 
Math. Sem. Univ. Hamburg. 72 (2002) 235–250. 
https://doi.org/10.1007/BF02941674.
G.P. Nagy, On the structure and number of small Frattini Bol 2-loops, 
Math. Proc. Cambridge Philos. Soc. 141 (2006) 409–419. 
https://doi.org/10.1017/S0305004106009625.
G.P. Nagy, A class of simple proper Bol loops, Manuscripta Math. 127 
(2008) 81–88. https://doi.org/10.1007/s00229-008-0188-5.
G.P. Nagy, A class of finite simple Bol loops of exponent 2, Trans. 
Amer. Math. Soc. 361 (2009) 5331–5343. 
https://doi.org/10.1090/S0002-9947-09-04646-7.

If you have some specific interest, feel free to contact me directly.

Best regards,

Gabor


On 2022. 06. 20. 16:13, Kurosh Mavaddat Nezhaad wrote:
> Dear All,
> I am working on loop theory, I would like to know the algorithm(s) that GAP
> used for constructing Bol loops, any address of papers and literature would
> be highly appreciated.
> With kind regards,
> Kuroš Mavaddat Nežâd
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