Hirsch length
= Hirsch length
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{title2=$h(G)$}
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The Hirsch length of a <polycyclic group> counts infinite cyclic factors in a polycyclic series. Refinement shows it is independent of the series, additive in extensions, and unchanged in finite-index subgroups. A finite-index <poly-infinite cyclic group> has one infinite cyclic factor for each unit of Hirsch length.