I need to put a reference about the classical result that a f.g. group of polynomial growth has growth which is exactly polynomial.

Talking personally with people and also here in A question about groups of intermediate growth, it seems that the result is attributed to Gromov and Pansu. In particular Gromov proved that a group of polynomial growth is virtually nilpotent and Pansu proved, in a paper in Ergodic Th & Dyn Systems that goes back to 1983, that a nilpotent group has exactly polynomial growth (is this right?)

Now, reading the introduction of http://de.arxiv.org/PS_cache/arxiv/pdf/1011/1011.5266v2.pdf, Bartholdi and Erschler say that the result is due to Guivarch (without reference) and Bass (in 1972).

So I am now little confused... who proved this theorem?

I guess that the problem is that nobody proved that theorem in this form. In this case, can anybody tell me a short history of the result, in such a way not to write wrong things?

Thank you in advance,

Valerio