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,i ∈I, 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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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
- Normal Subgroup
- Nilpotent Group
- Prime Divisor
- Wreath Product
- Finite Order