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Published online by Cambridge University Press: 20 January 2009
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.
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
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