Coverings of the smallest Paige loop
Stephen M.III Gagola
DOI: 10.1007/s10801-011-0284-6
Abstract
By investigating the construction of the split Cayley generalized hexagon, H(2), we get that there do not exist five distinct hexagon lines each a distance two apart from each other. From this we prove that the smallest Paige loop has a covering number of seven and that its automorphism group permutes these coverings transitively.
Pages: 607–615
Keywords: keywords covering number; Moufang loop; generalized hexagon; split Cayley hexagon
Full Text: PDF
References
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2. Chein, O.: Moufang loops of small order I. Trans. Am. Math. Soc. 188, 31-51 (1974)
3. Cohen, A.M., Tits, J.: On generalized hexagons and a near octagon whose lines have three points. Eur. J. Comb. 6, 13-27 (1985)
4. Detomi, E., Lucchini, A.: On the structure of primitive n-sum groups. CUBA Math. J. 10, 195-210 (2008)
5. Foguel, T., Kappe, L.C.: On loops covered by subloops. Expo. Math. 23, 255-270 (2005)
6. Gagola, S.M. III: Subloops of the unit octonions. Acta Sci. Math. 72, 837-861 (2006)
7. Gagola, S.M. III: The development of Sylow p-subloops in finite Moufang loops. J. Algebra 322(5), 1565-1574 (2009)
8. Gagola, S.M. III: The number of Sylow p-subloops in finite Moufang loops. Commun. Algebra 38(4), 1436-1448 (2010)
9. Kantor, W.M.: Generalized quadrangles associated with G2(q). J. Comb. Theory, Ser. A 29, 212-219 (1980)
10. Liebeck, M.W.: The classification of finite simple Moufang loops. Math. Proc. Camb. Philos. Soc.
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