A Short Note on Disjointness Conditions for Triples of Group Subsets Satisfying the Triple Product Property

(See [2] for a basic de nition.) The TPP property for the triple (S, T, U) is invariant under permutations of the triple, that is, the permuted triples (S,U, T ), (T, S, U), (T,U, S), (U, S, T ), (U, T, S) all satisfy the TPP i (S, T, U) satis es the TPP, ([6], p. 45). We denote by =(G) the set of all TPP triples of G, and by =(G)/Sym3 the set of equivalence classes of =(G) under the equivalence relation that two TPP triples of G are equivalent i they are permutations of each other. =(G) is non-empty since it always the contains the TPP triple (G, {1G}, {1G}), ([6], p. 44).