... Thus, the the existence of aSOMA(n − 1,n) is equivalent to the existence of n − 1 MOLS of order n, and henceto the existence of a projective plane of order n.Ifnis a power of a prime then thereexists ... more of: a row permutation, a column permutation, and renaming symbols.In this paper we study the structure of a SOMA, and then report on the use of computational group theory and graph theory ... k,n)ofA.ThusAis inde-composable if and only if A and ∅ are the only subSOMAs of A. The disjoint union of subSOMAs of A is a subSOMA, and it is easy to see that if B and C are subSOMAs of A,thenB∩Cis...