ISSN:
1420-8903
Keywords:
39B50
;
20N05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary V. D. Belousov (1925–88) made numerous contributions to the study of quasigroups. In particular, his lengthy 1966 paper “Balanced identities in quasigroups” [4] contains what has been described as a “very significant” and “remarkable” theorem [11, pp. 68–69]. Remarkable though it was, this theorem provided only a partial answer to the question as to which balanced equations on quasigroups gave rise to group isotopes. Although not specifically addressed in the paper [12], a characterization of the balanced equations in question may be derived from a generalization of Belousov's Theorem due to E. Falconer. The first author explicitly solved the problem in 1979; however his characterization was of a technical nature and depended on machinery developed over three papers [13]. In 1985 Belousov found a characterization which is not only elegant but also lends itself to a simple proof [5]. The purpose of this paper is to provide sufficient background for the non specialist to understand and enjoy what we too would describe as “a remarkable theorem”.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01818477
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