Geodesic
Six Moufang Loops of Units
Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 951-973

Voir la notice de l'article provenant de la source Cambridge University Press

We compute the loops of units in the integral alternative loop rings of six Moufang loops. Four of these are subloops of the loop of matrices of determinant one in Zorn's vector matrix algebra over a ring of integers while the remaining two are closely related to this interesting algebra. This paper thus serves, in part, to highlight a Moufang analogue of SL(2, Z) which the author suggests is worthy of further study.
DOI : 10.4153/CJM-1992-059-7
Mots-clés : Primary: 20N05, 17D05, secondary: 16A25 
Goodaire, Edgar G. Six Moufang Loops of Units. Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 951-973. doi: 10.4153/CJM-1992-059-7
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[1] 1. Allen, P.J. and Hobby, C., A characterization of units in Z[A4], J. Algebra 66(1980), 534–543. Google Scholar

[2] 2. Allen, P.J. and Hobby, C., A characterization of units in Z[S4], Comm. Algebra (7) 16 (1988), 1479–1505. Google Scholar

[3] 3. Chein, Orin, Moufang loops of small order, Mem. Amer. Math. Soc. (13) 197(1978). Google Scholar

[4] 4. Chein, Orin and Goodaire, Edgar G., Loops whose loop rings are alternative, Comm. Algebra. 14(1986), 293–310. Google Scholar

[5] 5. Goodaire, Edgar G. and Milies, César Polcino, Torsion units in alternative loop rings, Proc. Amer. Math. Soc. 107(1989), 7–15. Google Scholar

[6] 6. Goodaire, Edgar G. and Parmenter, M.M., Units in alternative loop rings, Israel J. Math. (2). 53(1986), 209–216. Google Scholar

[7] 7. Goodaire, Edgar G. and Parmenter, M.M., Semi-simplicity of alternative loop rings, Acta Math. Hungar. (3-4). 50(1987), 241–247. Google Scholar

[8] 8. Graham Higman, The units of group rings, Proc. London Math. Soc. (2) 46(1940), 231–248. Google Scholar

[9] 9. Hughes, I. and Pearson, K.R., The group of units of the integral group ring ZS3, Canad. Math. Bull. 15(1972), 529–534. Google Scholar

[10] 10. Eric Jespers and Guilherme Leal, A characterization of the unit loop of the integral loop ring ZM i6(Q, 2), to appear in J. Alg. Google Scholar

[11] 11. Eric Jespers and Guilherme Leal, Describing units of integral group rings of some 2-groups, Comm. Algebra (6) 19(1991), 1809–1827. Google Scholar

[12] 12. Martin Liebeck, W., The classification of finite simple Moufang loops, Math. Proc. Cambridge Philos. Soc.. 102(1987), 33–47. Google Scholar

[13] 13. Polcino, C.S. Milies, The group of units of the integral group ring ZD4, Bol. Soc. Brasil. Mat. (2) 4(1973), 85–92. Google Scholar

[14] 14. Lowell Paige, J., A class of simple Moufang loops, Proc. Amer. Math. Soc.. 7(1956), 471–482. Google Scholar

[15] 15. Parmenter, M.M., Torsion-free normal complements in unit groups of integral group rings, C.R. Math. Rep. Acad. Sci. Canada (4) XII(1990), 113–118. Google Scholar

[16] 16. Jiirgen Ritter and Sudarshan Sehgal, K., Construction of units in integral group rings of finite nilpotent groups, Trans. Amer. Math. Soc. (2). 324(1991), 603–621. Google Scholar

[17] 17. Sehgal, S.K., Topics in group rings, Marcel Dekker, New York, 1978. Google Scholar

[18] 18. Thomas, A.D. and G.V.Wood, Group tables, Shiva Publishing, Orpington, 1980. Google Scholar

[19] 19. Zhevlakov, K.A., Slin'ko, A.M., Shestakov, I.P. and Shirshov, A.I., Rings that are nearly associative, Academic Press, New York, 1982, Translated by Harry F. Smith. Google Scholar

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