Intersection graphs of almost subnormal subgroups in general skew linear groups
Résumé
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*.
Origine | Fichiers produits par l'(les) auteur(s) |
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