Abstract
A group G is called polycyclic (resp. polycyclic-by-finite, resp. poly-infinite-cyclic) if it admits a subnormal series, that is, a sequence of subgroups \(\left\{ {1_{G} } \right\} = H_{0} \le H_{1} \le H_{2} \le \cdots \le H_{n} = G\) such that Hi is normal in \(H_{i + 1}\), with \(H_{i + 1} /H_{i}\) a (finite or infinite) cyclic (resp. (infinite) cyclic or finite, resp. infinite cyclic) group for each \(0 \le i \le n - 1\).
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Ceccherini-Silberstein, T., D’Adderio, M. (2021). Polycyclic Groups. In: Topics in Groups and Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-88109-2_5
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DOI: https://doi.org/10.1007/978-3-030-88109-2_5
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