V članku dokažemo, da vkolikor ultrafilter ▫$\mathcal{L}$▫ ni koherenten ▫$Q$▫-točki, potem vsaka analitična ne-▫$\sigma$▫-omejena topološka grupa ▫$G$▫ dopušča naraščajočo verigo ▫$\langle G_\alpha ...\colon \alpha < \mathfrak{b} (\mathcal{L}) \rangle$▫ njenih pravih podgrup, ki ima naslednje lastnosti: (i) ▫$\bigcup_\alpha G_\alpha = G$▫; in (ii) za vsako ▫$\sigma$▫-omejeno podgrupo ▫$H$▫ grupe ▫$G$▫ obstaja takšen ▫$\alpha$▫, da velja ▫$H \subset G_\alpha$▫. V primeru grupe ▫${\rm Sym}(\omega)$▫ vseh permutacij ▫$\omega$▫ s topologijo, ki je podedovana iz ▫$\omega^\omega$▫ naši rezultati izboljšujejo prejšnje rezultate S. Thomasa.
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