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Construct a finite nilpotent loop with no finite basis for its laws. Proposed: by M. R. Vaughan-Lee in the Kourovka Notebook of Unsolved Problems in Group Theory; Comment: There is a finite loop with no finite basis for its laws (Vaughan-Lee, 1979) but it is not nilpotent.
The integers Z (or the rationals Q or the reals R) with subtraction (−) form a quasigroup. These quasigroups are not loops because there is no identity element (0 is a right identity because a − 0 = a, but not a left identity because, in general, 0 − a ≠ a). The nonzero rationals Q × (or the nonzero reals R ×) with division (÷) form ...
Download as PDF; Printable version ... This category is intended for all unsolved problems ... List of problems in loop theory and quasigroup theory; List of unsolved ...
One can normalize a Cayley table of a quasigroup in the same manner as a reduced Latin square. Then the quasigroup associated to a reduced Latin square has a (two sided) identity element (namely, the first element among the row headers). A quasigroup with a two sided identity is called a loop. Some, but not all, loops are groups.
Problems in loop theory and quasigroup theory. Add languages. ... Download QR code; Print/export Download as PDF; Printable version;
In mathematics, the theory of Latin squares is an active research area with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Problems posed here appeared in, for instance, the Loops (Prague) conferences and the Milehigh (Denver) conferences.
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