Abstract
The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup. Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group of finite rank of infinite cyclic center, we provide a decomposition of G as the product of a generalized extraspecial ℤ-group and its center. By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial ℤ-groups, we finally obtain the structure and invariants of the group G.
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Acknowledgements
The authors would like to thank Prof. Derek J. S. Robinson for his useful comments and valuable suggestions. The authors also thank the referee for his/her helpful comments and suggestions contributed to the final version of this paper.
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Supported by NSFC (Grant Nos. 11631001, 11771129, 11971155 and 12071117)
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Liao, J., Liu, H.G., Xu, X.Z. et al. Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups. Acta. Math. Sin.-English Ser. 36, 1315–1340 (2020). https://doi.org/10.1007/s10114-020-9132-8
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DOI: https://doi.org/10.1007/s10114-020-9132-8