Geodesic
Schreier loops
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 759-786 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.
We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.
Classification : 20N05
Keywords: extension of loops; non-associative extension of groups; weak associativity properties of extensions; central extensions 
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}
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Nagy, Péter T.; Strambach, Karl. Schreier loops. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 759-786. http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a13/

[1] Birkenmeier, G., Davis, B., Reeves, K., Xiao, S.: Is a semidirect product of groups necessarily a group?. Proc. Amer. Math. Soc. 118 (1993), 689-692. | DOI | MR | Zbl

[2] Birkenmeier, G., Xiao, S.: Loops which are semidirect products of groups. Comm. in Algebra 23 (1995), 81-95. | DOI | MR | Zbl

[3] Chein, O.: Moufang loops of small order I. Trans. Amer. Math. Soc. 188 (1974), 31-51. | DOI | MR | Zbl

[4] Chein, O.: Moufang loops of small order. Mem. Amer. Math. Soc. 13 (1978), 31-51. | MR | Zbl

[5] Chein, O.: Examples and methods of construction, Chapter II in Quasigroups and Loops: Theory and Applications. O. Chein, H. O. Pflugfelder, J. D. H. Smith 27-93 Heldermann Verlag, Berlin (1990). | MR

[6] Chein, O., Goodaire, E. G.: A new construction of Bol loops of order $8k$. Journal of Algebra 287 (2005), 103-122. | DOI | MR | Zbl

[7] Csörgő, P., Drápal, A.: Left conjugacy closed loops of nilpotency class two. Results Math. 47 (2005), 242-265. | DOI | MR

[8] Figula, A.: $3$-dimensional Bol loops as sections in non-solvable Lie groups. Forum Math. 17 (2005), 431-460. | DOI | MR | Zbl

[9] Figula, A.: $3$-dimensional loops on non-solvable reductive spaces. Adv. Geom. 5 (2005), 391-420. | DOI | MR | Zbl

[10] Figula, A.: $3$-dimensional Bol loops corresponding to solvable Lie triple systems. Publ. Math. Debrecen 70 (2007), 59-101. | MR | Zbl

[11] Figula, A., Strambach, K.: Loops which are semidirect products of groups. Acta Math. Hungar. 114 (2007), 247-266. | DOI | MR | Zbl

[12] Kinyon, M. K., Kunen, K.: The structure of extra loops. Quasigroups Related Systems 12 (2004), 39-60. | MR | Zbl

[13] Kinyon, M. K., Kunen, K., Phillips, J. D.: A generalization of Moufang and Steiner loops. Algebra Universalis 48 (2002), 81-101. | DOI | MR | Zbl

[14] Kinyon, M. K., Phillips, J. D., Vojtěchovský, P.: C-loops; extensions and constructions. J. Algebra Appl. 6 (2007), 1-20. | DOI | MR

[15] Kinyon, M. K., Phillips, J. D., Vojtěchovský, P.: When is the commutant of a Bol loop a subloop. Trans. Amer. Math. Soc. 360 (2008), 2393-2408. | DOI | MR

[16] Kurosh, A. G.: The Theory of Groups, Vol. 2, transl. from Russian by K. A. Hirsch. Chelsea Publishing Co., New York (1956). | MR

[17] Nagy, G. P.: Algebraic commutative Moufang loops. Forum Math. 15 (2003), 37-62. | MR | Zbl

[18] Nagy, P. T., Strambach, K.: Loops in Group Theory and Lie Theory, Expositions in Mathematics 35. Walter de Gruyter, Berlin-New York (2002). | MR

[19] Pflugfelder, H. O.: Quasigroups and Loops: An Introduction. Heldermann Verlag, Berlin (1990). | MR

[20] Schreier, O.: Über die Erweiterung von Gruppen I. Monatshefte f. Math. 34 (1926), 165-180. | MR

[21] Schreier, O.: Über die Erweiterung von Gruppen II. Abh. Math. Sem. Univ. Hamburg 4 (1926), 321-346. | DOI

[22] Suvorov, N. M., Krjuckov, N. I.: Examples of certain quasigroups and loops that permit only the discrete topologization. Russian Sib. Mat. Zh. 17 (1976), 471-473. | MR

[23] Suvorov, N. M.: A commutative IP-loop that admits only discrete topologization. Russian Sib. Mat. Zh. 32 (1991), 193. | MR

[24] Suzuki, M.: Group Theory, Vol. 1. Grundlehren der Mathematischen Wissenschaften 10, Springer Verlag, Berlin-New York (1982). | MR

[25] Winterroth, E.: Right Bol loops with a finite dimensional group of multiplications. Publ. Math. Debrecen 59 (2001), 161-173. | MR | Zbl