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SM ISO690:2012 COTE, B., HARVILL, B., HUHN, Michael, KIRCHMAN, A.. Classification of loops of generalized
Bol-Moufang type. In: Quasigroups and Related Systems, 2011, vol. 19, nr. 2(26), pp. 193-206. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 19, Numărul 2(26) / 2011 / ISSN 1561-2848 | ||||||
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Pag. 193-206 | ||||||
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A loop identity α = ß is of Bol-Moufang type if the same 3 variables appear on both sides of the equal sign in the same order, one of the variables appears twice on both sides and the remaining two variables appear once on both sides. One
can generalize this definition by allowing different variable orders on either side of the identity, e.g. ((xx)y)z = ((y(xz)). There are 1215 nontrivial identities of this type. Loop varieties axiomatized by a single identity of this type are said to be of generalized Bol-Moufang type. We show that there are 48 such varieties: the 14 varieties of Bol-Moufang
type [13], the 6 varieties of commutative Bol-Moufang type, and 28 new varieties. |
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