 
Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 354, Number 8, Pages 33293348
S 00029947(02)029859
Article electronically published on April 3, 2002
SOLVABLE GROUPS WITH POLYNOMIAL DEHN FUNCTIONS
G. N. ARZHANTSEVA AND D. V. OSIN
Abstract. Given a finitely presented group H, finitely generated subgroup B
of H, and a monomorphism : B H, we obtain an upper bound of the Dehn
function of the corresponding HNNextension G = H, t  t1Bt = (B)
in terms of the Dehn function of H and the distortion of B in G. Using
such a bound, we construct first examples of nonpolycyclic solvable groups
with polynomial Dehn functions. The constructed groups are metabelian and
contain the solvable BaumslagSolitar groups. In particular, this answers a
question posed by Birget, Ol'shanskii, Rips, and Sapir.
1. Introduction
Recall that the Dehn function of a finitely presented group G = Y  R is the
smallest function : N N with the following property. For any word w over
Y Y1
representing the identity in G, there exists a van Kampen diagram over
