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Logarithmetics of Finite Quasigroups (II)

Published online by Cambridge University Press:  20 January 2009

Helen Popova
Helen Popova
Affiliation:
Department of Mathematics, University of Aberdeen.
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In the first paper of this series (L.Q.I)1 we have shown that the logarithmetic LQ of a finite quasigroup Q is a quasigroup with respect to addition and that it is a subdirect union of the logarithmetics of the elements of Q.

In this second part we shall discuss further the structure of LQ in its additive aspect, and obtain results concerning the order N of LQ. For plain quasigroups (§3) the structure of LQ(-\-) is studied in more detail and it is shown that N is a power of n, the order of Q.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 3 , July 1956 , pp. 109 - 115
Copyright
Copyright © Edinburgh Mathematical Society 1956

References

1 Popova, H., “Logarithmetics of finite quasigroups (I)”, Proc. Edinburgh Math. Soc. (2), 9 (1954), 74–81.CrossRefGoogle Scholar

2 Bruck, R. H., “Simple quasigroups”, Bull. American Math. Soc., 50 (1944), 769–781.CrossRefGoogle Scholar