Abstract
In the course of a recent investigation by the author [1] it was noted that the number of complete mappings (transversals) of each of the non-cyclic groups of order 8 was 364. Furthermore, it was found that both of the non-abelian groups of order 8 possessed exactly 128 near-complete mappings. These surprising results motivated an investigation into why this was the case. In the present paper we show why both of the non-abelian groups of order 8 possess the same number of complete and near-complete mappings. It is also shown why both of the non-cyclic abelian groups of order 8 possess the same number of complete mappings.
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