Geodesic
Asymptotic growth of averaged Dehn functions for nilpotent groups
Algebra i logika, Tome 46 (2007) no. 1, pp. 60-74

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It is proved that in any finite representation of any finitely generated nilpotent group of nilpotency class $l\geqslant1$, the averaged Dehn function $\sigma(n)$ is subasymptotic w.r.t. the function $n^{l+1}$. As a consequence it is stated that in every finite representation of a free nilpotent group of nilpotency class $l$ of finite rank $r\geqslant2$, the Dehn function $\sigma(n)$ is Gromov subasymptotic.
Keywords: nilpotent group, averaged Dehn function. 
@article{AL_2007_46_1_a3,
     author = {V. A. Roman'kov},
     title = {Asymptotic growth of averaged {Dehn} functions for nilpotent groups},
     journal = {Algebra i logika},
     pages = {60--74},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_1_a3/}
}
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V. A. Roman'kov. Asymptotic growth of averaged Dehn functions for nilpotent groups. Algebra i logika, Tome 46 (2007) no. 1, pp. 60-74. http://geodesic.mathdoc.fr/item/AL_2007_46_1_a3/