TITLE: Who proved that a group of polynomial growth has growth exactly polynomial?
QUESTION [7 upvotes]: 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

REPLY [6 votes]: Guivarc'h certainly did prove such a result, see
MR0302819 (46 #1962) 
Guivarc'h, Yves
Groupes de Lie à croissance polynomiale. (French) 
C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A1695–A1696. 
22E15 
As did Bass:
MR0379672 (52 #577) 
Bass, H.
The degree of polynomial growth of finitely generated nilpotent groups. 
Proc. London Math. Soc. (3) 25 (1972), 603–614.