Completely Reducible Linear Groups Over a Quaternion Division Algebra that Contain a Root Subgroup

DOI10.1080/00927870601074798zbMath1118.20049OpenAlexW2109724225MaRDI QIDQ3435941

Evgenii L. Bashkirov

Publication date: 8 May 2007

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870601074798

zbMATH Keywords

skew linear groupsroot subgroupsquaternion division algebrascompletely reducible subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Other matrix groups over rings (20H25)

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Cites Work

• Irreducible linear groups of degree four over a quaternion division algebra that contain a subgroup \(\text{diag}(T_3(K,\Phi_0),1)\).
• Groups generated by k-transvections
• Groups generated by \(k\)-root subgroups
• On linear groups containing the commutator subgroup of an orthogonal group of index greater than 1
• Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii
• Subgroups generated by root-elements of groups generated by \(k\)-root subgroups
• Linear groups containing a root subgroup
• Subgroups of classical groups generated by transvections or Siegel transvections. I: Embeddings in linear groups
• On subgroup of the special linear group of degree 2 over an infinite field
• Irreducible Linear Groups of Degree 3 Over a Quaternion Division Ring Containing a Root Subgroup
• Some Completely Reducible Linear Groups over a Quaternion Division Ring Containing a Root Subgroup
• Irreducible Linear Groups of Degree Four over a Quaternion Division Algebra that Contain a Root Subgroup
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