Geodesic
Loops of Bol-Moufang type with a subgroup of index two
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 71-83 
M. K. Kinyon; J. D. Phillips; P. Vojtěchovský. Loops of Bol-Moufang type with a subgroup of index two. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 71-83. http://geodesic.mathdoc.fr/item/BASM_2005_3_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We describe all constructions for loops of bol-moufang type analogous to the chein construction $m(g,*,g_0)$ for moufang loops.

[1] Bruck R. H., A Survey of Binary Systems, third printing, corrected, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, 20, Springer-Verlag, 1971 | MR | Zbl

[2] De Barros L. G. X., Juriaans S. O., “Some loops whose loop algebras are flexible, II”, International Journal of Mathematics, Game Theory and Algebra, 8:1, 73–80 | MR | Zbl

[3] Chein O., “Moufang loops of small order”, Mem. Amer. Math. Soc., 13, no. 197, 1978 | MR

[4] Fenyves F., “Extra loops. II: On loops with identities of Bol-Moufang type”, Publ. Math. Debrecen, 16 (1969), 187–192 | MR

[5] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.3, , Aachen, St Andrews, 1999 Visit http://www-gap.dcs.st-and.ac.uk/g̃ap

[6] Pflugfelder H. O., Quasigroups and Loops: Introduction, Sigma series in pure mathematics, 7, Heldermann Verlag, Berlin, 1990 | MR | Zbl

[7] Phillips J. D., Vojtěchovský P., “C-loops: an introduction”, Publ. Math. Debrecen, 68:1-2 (2006), 115–137 | MR | Zbl

[8] Phillips J. D., Vojtěchovský P., “The varieties of loops of Bol-Moufang type”, Algebra Universalis, 54:3 (2005), 259–271 | DOI | MR | Zbl

[9] Vojtěchovský P., “On the uniqueness of loops $M(G,2)$”, Comment. Math. Univ. Carolin., 44:4 (2003), 629–635 | MR | Zbl

[10] Vojtěchovský P., “A class of Bol loops with a subgroup of index two”, Comment. Math. Univ. Carolin., 45:2 (2004), 371–381 | MR | Zbl