It is known that the minimum number of generators d(G^n) of the n-th direct power G^n of a non-trivial finite group G tends to infinity with n. This prompts the question: in which ways can the sequence {d(G^n)} tend to infinity? This question was first asked by Wiegold who almost completely answered it for finitely generated groups during the 70's. The question can then be generalised to any algebraic structure and this is still an open problem currently being researched. I will talk about some of the results obtained so far and will try to explain some of the methods used to obtain them, both for groups and for the more general algebraic structure setting.
