Izbash, V. I. Quasigroups with distributive lattice of subquasigroups. (Russian) Zbl 0746.20054 Mat. Issled. 113, 42-51 (1990). The quasigroups (loops) mentioned in the title are called \(D\)-quasigroups (\(D\)-loops). The author proves the following theorems. Every diassociative \(D\)-loop is a group. If \(n\in N\), \(n\geq 3\) or \(n=\aleph_ 0\) there exists a cyclic \(D\)-quasigroup of order \(n\) which is not a one- sided loop; there also exists a medial one-sided \(D\)-loop of order \(n\) which is not a loop. There exists a commutative and non-associative \(D\)- loop of order \(2n\). There also exists a commutative and non-associative loop of order \(2n\) for which the equality \(x^ 2=1\) holds. Reviewer: M.Csikós (Gödöllö) MSC: 20N05 Loops, quasigroups 06D05 Structure and representation theory of distributive lattices Keywords:distributive lattice of subquasigroups; \(D\)-quasigroups; \(D\)-loops; diassociative \(D\)-loop; cyclic \(D\)-quasigroup; medial one-sided \(D\)-loop PDFBibTeX XMLCite \textit{V. I. Izbash}, Mat. Issled. 113, 42--51 (1990; Zbl 0746.20054) Full Text: EuDML