Non-polycyclic-by-finite maximal subgroup theorem for skew linear groups

Let DD be an infinite division ring, let nn be a natural number, and let MM be a maximal subgroup of GLn(D)\mathrm{GL}_n(D). Non-polycyclic-by-finite maximal subgroup theorem. If n=1n=1 or the center of DD contains at least five elements, then MM cannot be polycyclic-by-finite. The source presents this as a main result in its study of polycyclic-by-finite skew linear groups, following the observation that GLn(D)\mathrm{GL}_n(D) itself cannot be polycyclic-by-finite.

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Primary source

M. Ramezan-Nassab and D. Kiani, “Nilpotent and polycyclic-by-finite maximal subgroups of skew linear groups”, arXiv:1307.5498 (2013).

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