2017•St Petersburg Mathematical JournalOpen access

Free subgroups in almost subnormal subgroups of general skew linear groups

Nguyen Kim Ngoc, Mai Hoang Bien, Bui Xuan Hai

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Abstract

Let $D$ be a weakly locally finite division ring and $n$ a positive integer. The problem under study concerns the existence of noncyclic free subgroups in noncentral almost subnormal subgroups of the general linear group $\operatorname {GL} _n(D)$. Further, some applications are also investigated. In particular, all infinite finitely generated almost subnormal subgroups of $\operatorname {GL} _n(D)$ are described.

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Let $D$ be a weakly locally finite division ring and $n$ a positive integer. The problem under study concerns the existence of noncyclic free subgroups in noncentral almost subnormal subgroups of the general linear group $\operatorname {GL} _n(D)$. Further, some applications are also investigated. In particular, all infinite finitely generated almost subnormal subgroups of $\operatorname {GL} _n(D)$ are described.

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Available abstract

Let $D$ be a weakly locally finite division ring and $n$ a positive integer. The problem under study concerns the existence of noncyclic free subgroups in noncentral almost subnormal subgroups of the general linear group $\operatorname {GL} _n(D)$. Further, some applications are also investigated. In particular, all infinite finitely generated almost subnormal subgroups of $\operatorname {GL} _n(D)$ are described.

Key concepts: Mathematics, Skew, Integer (computer science), Combinatorics, Finitely-generated abelian group, Division (mathematics), Ring (chemistry), Group (periodic table)

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