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On Multiplicative Properties of Families of Complexes of Certain Loops

  • Meir Steinberger (a1)

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It is well-known that if is a quotient group of a group G, then (i) is a partition of G, and (ii) the usual complex product (in the usual sense of multiplication of complexes) of every pair of members of is a member of . There arises the question whether, conversely, (i) and (ii), perhaps in a weaker form, suffice for to be a quotient group of G.

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References

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1. Artzy, R., Crossed inverse and related loops, Trans. Amer. Math. Soc. 91 (1959), 480492.
2. Bates, G. E. and Kiokemeister, K., A note on homomorphic mappings of quasigroups into multiplicative systems, Bull. Amer. Math. Soc. 54 (1948), 11801185.
3. Bruck, R. H., A survey of binary systems (Springer Verlag, Berlin, 1958).
4. Ginzburg, A., Systèmes multiplicatifs de relations. Boucles quasi-associatives, C. R. Acad. Sci. Paris Sér. A-B 250 (1960), 14131416.
5. Huthnance, E. D., A theory of generalized Moufang loops, Ph.D. Thesis, Georgia Institute of Technology, 1968.
6. Osborn, J. M., Loops with the weak inverse property, Pacific J. Math. 10 (1960), 295304.
7. Robinson, D. A., Bol loops, Trans, Amer. Math. Soc. 123 (1966), 341354.
8. Zassenhaus, H. J., The theory of groups, 2nd ed. (Chelsea Publ. Co., New York, 1958).
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On Multiplicative Properties of Families of Complexes of Certain Loops

  • Meir Steinberger (a1)

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