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The residual nilpotency of the augmentation ideal and the residual nilpotency of some classes of groups

Abstract

The following theorem is proved: LetG be any group. Then the augmentation ideal ofZG is residually nilpotent if and only ifG is approximated by nilpotent groups without torsion or discriminated by nilpotent pi,-groups,iI, of finite exponents. This theorem is applied to obtain conditions under which the groupsF/N′ are residually nilpotent whereF is a free non-cyclic group and N◃F.

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Correspondence to A. I. Lichtman.

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Lichtman, A.I. The residual nilpotency of the augmentation ideal and the residual nilpotency of some classes of groups. Israel J. Math. 26, 276–293 (1977). https://doi.org/10.1007/BF03007647

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Keywords

  • Normal Subgroup
  • Nilpotent Group
  • Prime Divisor
  • Wreath Product
  • Finite Order