Le Van Chua | Searcharxiv

arXiv2026

On Locally Generalized radical linear groups over rings

In this paper, we investigate the structure of locally generalized radical linear groups over certain non-commutative rings and algebras. The base rings and algebras we consider include division rings, left artinian rings, locally finite algebras over fields, and PI-algebras over fields. Among various results, we get the positive answers to the General Burnside Problem and to Baer's Conjecture for some particular cases of linear groups.

math.RA↗

arXiv2020

Intersection graphs of almost subnormal subgroups in general skew linear groups

Let $D$ be a division ring, $n$ a positive integer, and GL$_n(D)$ the general linear group of degree $n$ over $D$. In this paper, we study the induced subgraph of the intersection graph of GL$_n(D)$ generated by all non-trivial proper almost subnormal subgroups of GL$_n(D)$. We show that this subgraph is complete if it is non-null. This property will be used to study subgroup structure of a division ring. In particular, we prove that every non-central almost subnormal subgroup of the multiplicative group $D^*$ of a division ring $D$ contains a non-central subnormal subgroup of $D^*$.

math.RA↗