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arXiv · 1808.08453

On free subgroups in maximal subgroups of skew linear groups

Bui Xuan Hai·Huynh Viet Khanh
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Abstract

The study of the existence of free groups in skew linear groups have been begun since the last decades of the 20-th century. The starting point is the theorem of Tits (1972), now often is referred as Tits' Alternative, stating that every finitely generated subgroup of the general linear group $\GL_n(F)$ over a field $F$ either contains a non-cyclic free subgroup or it is solvable-by-finite. In this paper, we study the existence of non-cyclic free subgroups in maximal subgroups of an almost subnormal subgroup of the general skew linear group over a locally finite division ring.

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Bui Xuan Hai, Huynh Viet Khanh. 2019-02-19. On free subgroups in maximal subgroups of skew linear groups. https://doi.org/10.1142/s0218196719500164

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