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On the product of an abelian group and a nilpotent group

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Abstract

We study the structure of the product of an Abelian group and a nilpotent group. Conditions for the existence of a normal subgroup in one of the factors are given. These conditions generalize the known results on the product of two Abelian groups. The statements obtained are used to describe the structure of a product of an infinite cyclic subgroup and a periodic nilpotent subgroup.

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Authors
  1. O. V. Gorodnik
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1165–1171, September, 1999.

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Gorodnik, O.V. On the product of an abelian group and a nilpotent group. Ukr Math J 51, 1314–1320 (1999). https://doi.org/10.1007/BF02592998

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  • DOI: https://doi.org/10.1007/BF02592998

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