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Finite Bol loops

Published online by Cambridge University Press:  24 October 2008

R. P. Burn
Affiliation:
Homerton College, Cambridge

Extract

In this paper, we prove that, for any prime p, a Bol loop of order 2p or of order p2 is necessarily a group, and we show that there exist exactly six non-associative Bol loops of order 8.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Albert, A. A.Quasigroups I. Trans. Amer. Math. Soc. 54 (1943), 507519.Google Scholar
(2)Albert, A. A.Quasigroups II. Trans. Amer. Math. Soc. 55 (1944), 401419.Google Scholar
(3)Bol, G.Gewebe und Gruppen. Math. Ann. 114 (1937), 414431.Google Scholar
(4)Bruck, R. H.A survey of binary systems (Berlin, Springer-Verlag, 1958).Google Scholar
(5)Chein, O. and Pflugfelder, H. O.The smallest Moufang loop. Arch. Math. 22 (1971), 573576.Google Scholar
(6)Glauberman, G.On loops of odd order II, J. Algebra 8 (1968), 393414.Google Scholar
(7)Robinson, D. A.Bol loops. Trans. Amer. Math. Soc. 123 (1966), 341354.Google Scholar