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Intersection graphs of almost subnormal subgroups in general skew linear groups

Abstract : 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*.
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https://hal.archives-ouvertes.fr/hal-02997959
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Submitted on : Tuesday, November 10, 2020 - 12:19:25 PM
Last modification on : Sunday, June 26, 2022 - 2:56:30 AM
Long-term archiving on: : Friday, February 12, 2021 - 12:17:04 PM

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  • HAL Id : hal-02997959, version 1

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Xuan Hai Bui, Binh-Minh Bui-Xuan, Le Van Chua, Mai Hoang Bien. Intersection graphs of almost subnormal subgroups in general skew linear groups. 2020. ⟨hal-02997959⟩

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