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 groups
in
which, for every subset
of
of 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 subgroup
with finite index such that the nilpotency class of
is
bounded by a function of
, where
, is the torsion subgroup of
.
(2) If
be
generated, then
has a normal nilpotent subgroup
whose index and the nilpotency class are bounded
by a function of
.
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