Free subgroups in almost subnormal subgroups of general skew linear groups
Nguyen Kim Ngoc, Mai Hoang Bien, Bui Xuan Hai
Abstract
Open-access reader
Nguyen Kim Ngoc, Mai Hoang Bien, Bui Xuan Hai
Abstract
Open-access reader
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.
Key concepts: Mathematics, Skew, Integer (computer science), Combinatorics, Finitely-generated abelian group, Division (mathematics), Ring (chemistry), Group (periodic table)