Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Pages 000--000
S 0002­9947(XX)0000­0
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 = hH; t j t \Gamma1 Bt = /(B)i
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.
Section de Math' ematiques, Universit' e de Gen` eve, CP 240, 1211 Gen` eve 24, Switzer­
land
E­mail address: Goulnara.Arjantseva@math.unige.ch
Department of High Algebra, MEHMAT, Moscow State University, 119899 Moscow,
Russia
E­mail address: Denis.Osin@mtu­net.ru

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

Collections: Mathematics