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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 354, Number 8, Pages 3329­3348
S 0002-9947(02)02985-9
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 HNN-extension G = H, t | t-1Bt = (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 non-polycyclic solvable groups
with polynomial Dehn functions. The constructed groups are metabelian and
contain the solvable Baumslag-Solitar 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 Y-1
representing the identity in G, there exists a van Kampen diagram over

  

Source: Arzhantseva, Goulnara N. - Section de Mathématiques, Université de Genève

 

Collections: Mathematics