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A Note on Cayley Loops

Published online by Cambridge University Press:  20 November 2018

A. Ginzburg
A. Ginzburg*
Affiliation:
Technion, Israel Institute of Technology Haifa, Israel
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In § 1 the existence of two non-isotopic loops satisfying the same system of relations is proved: C1 is isomorphic to the well-known Cayley loop (see 1 or 6); C2 seems not to have been mentioned in the literature. In § 2 a characterization of the second type is given in terms of Tamari's generalized normal multiplication table (7; 8) as a complete symmetric quasiregular partition, i.e., a quasi-associative loop (4, 5), or a so-called near-group (9). In § 3 these distinctions are followed by comparing the corresponding algebras.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 77 - 81
Copyright
Copyright © Canadian Mathematical Society 1964

References

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