Free subgroups in maximal subgroups ofGLn(D)

The study of the existence of free groups in skew linear groups have begun since the last decades of the 20th century. The starting point is the theorem of Tits (1972), now often referred to as Tits’ Alternative, stating that every finitely generated subgroup of the general linear group [Formula: see text] over a field [Formula: see text] 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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Free subgroups in maximal subgroups of SLn(D)

Fallah-Moghaddam

2020

J. Algebra Appl.

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Given a non-commutative finite-dimensional [Formula: see text]-central division ring [Formula: see text], [Formula: see text] a subnormal subgroup of [Formula: see text] and [Formula: see text] a non-abelian maximal subgroup of [Formula: see text], then either [Formula: see text] contains a non-cyclic free subgroup or there exists a non-central maximal normal abelian subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] is a subfield of [Formula: see text], [Formula: see text] is Galois and [Formula: see text], also [Formula: see text] is a finite simple group with [Formula: see text].

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Free subgroups in maximal subgroups ofGL_n(D)

Cited by 4 publications

References 14 publications

Maximal subgroups of SL(D)

Maximal subgroups of SL(D)

Free subgroups in maximal subgroups of skew linear groups

Free subgroups in maximal subgroups of SLn(D)

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