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Numbers of d.g. nearrings on groups with special properties, e.g., dihedral groups

In 1982 ([24]), J.J. Malone published a result on the numbers of d.g. nearrings definable of the dihedral groups , n even. A search through the library of small nearrings revealed that there are in fact 24 d.g. nearrings definable on , the dihedral group of order 12, which is in contradiction to Malone's result, which predicts 20 nearrings on . We intend to report on this in detail in an upcoming paper ([20]).

Juergen Ecker
Wed May 13 09:13:56 CEST 1998