  In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix
multiplication. This involves finding large subsets S, T and U of a group G
satisfying the Triple Product Property (TPP) as a means to bound the exponent
$\omega$ of the matrix multiplication. We show that S, T and U may be be
assumed to contain the identity and be otherwise disjoint. We also give a much
shorter proof of the upper bound |S|+|T|+|U| <= |G|+2.
