ON MULTIPLICATION TABLES OF GROUPS THAT AGREE ON HALF OF THE COLUMNS AND HALF OF THE ROWS

Let G(o) and G(*) be two groups of finite order n, and suppose that each of the sets {u in G; uo v=u*v for all v in G} and {v in G; uo v=u*v for all u in G} has n/2 elements. Then G(*) can be obtained from G(o) by one of the two general constructions that are discussed in the paper.