Subcubic Growth of the Averaged Dehn Function for a Class 2 Nilpotent Group

We show that the averaged Dehn function with respect to each finite presentation of an arbitrary finitely generated class 2 nilpotent group is subcubic. For the finite rank 2 free class 2 nilpotent group this implies the subasymptoticity of the averaged Dehn function in the sense of M. Gromov, confirming his conjecture.Original Russian Text Copyright © 2005 Romankov V. A.The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00489) and the Scientific Program Universities of Russia of the Ministry for Education of the Russian Federation (Grant 362-05).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 663–672, May–June, 2005.