Abstract
The problem of tiling space by translates of certain star bodies, called ‘crosses’ and ‘semicrosses’, is intimately connected with finding a subsetA of a finite abelian groupG such that for a particular subset of the integersS each non-zero element ofG is uniquely expressible in the forms·g withs inS andg inA. This paper examines some of the algebraic questions raised; in particular it obtains bounds on the number of elements inS, constructs factorizations ofZ p n , and presents an example of a setS that factors no group.
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