On a Class of Residually Finite Groups
Taeri, B., (2003) On a Class of Residually Finite Groups. Bulletin of the Malaysian Mathematical Sciences Society, 26 (2). pp. 209-219. ISSN 0126-6705
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Official URL: http://math.usm.my/bulletin/pdf/v26n2/v26n2p7.pdf
Isfahan University of Technology, Dept. of Mathematics
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 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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