Volume 26 • Number 2 • 2003

On a Class of Residually Finite Groups
Bijan Taeri

Abstract. Let be positive integers and be non-zero integers. We denote by the class of groupsin
which, for every subsetofof cardinality , there exist a subset, with ,, and a function
, with such that where ,. The class
is defined exactly as , with additional conditions " whenever, where".
Let G be a finitely generated residually finite group. Here we prove that
(1) If , then has a normal nilpotent subgroupwith finite index such that the nilpotency class of is
bounded by a function of , where , is the torsion subgroup of .
(2) If be generated, thenhas a normal nilpotent subgroupwhose index and the nilpotency class are bounded
by a function of .

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