On 4 − T−quasigroups with exactly 20 distinct parastrophes [Articol]

Abstract

The T−forms and the spectrum of 4 − T−quasigroups with exactly 20 distinct parastrophes are considered in the present work. Characterizations of the spectra of finite binary quasigroups with a prescribed number of distinct parastrophes were given by C.C. Lindner and D. Steedly in [1]. Following the results of C.C. Lindner and D. Steedly, M. MacLeish proved that the maximum number of distinct parastrophes of an n−quasigroup (Q,A) is a divizor of (n+1)!, and obtained characterizations of the spectrum of finite ternary quasigroups with a prescribed (maximum) number of distinct parastrophes. Binary and ternary linear quasigroups over groups, with a given maximum number of distinct parastrophes have been studied by Belyavskaya, Rotari, Sokhatsky, Pirus, Fryz and others [4-8]. Characterizations of the general T−form of a 4−T−quasigroup with exactly 20 distinct parastrophes and some estimations of their spectrum are given in the present work.