A finite group G is said to be efficient if G has a presentation 〈 X | R 〉 where |R| = |X|+rank(M(G)) where M(G) is the Schur multiplier of G; see for example [14]. The efficiency of direct powers, G, of a finite group G has been studied over a number of years, see for example [5], [8] and [14]. In [6] the problem of proving that G is efficient for all n ∈… (More)