On the non-triviality of \(G(D)\) and the existence of maximal subgroups of \(\text{GL}_1(D)\).

DOI10.1016/j.jalgebra.2004.11.020zbMath1099.20027OpenAlexW2026469751MaRDI QIDQ1770474

M. Mahdavi-Hezavehi, T. Keshavarzipour

Publication date: 7 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.11.020

zbMATH Keywords

maximal subgroupsquaternion algebrasdivision ringssplitting fields

Mathematics Subject Classification ID

Maximal subgroups (20E28) Other matrix groups over rings (20H25) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (5)

Nontriviality of certain quotients of \(K_1\) groups of division algebras. ⋮ A Criterion for the Triviality ofG(D) and Its Applications to the Multiplicative Structure ofD ⋮ UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS ⋮ On maximal subgroups of the multiplicative group of a division algebra. ⋮ A Decomposition Theorem for CK₁of Central Simple Algebras

Cites Work

• On the existence of normal maximal subgroups in division rings
• Extending valuations to algebraic division algebras
• Finite-Dimensional Division Algebras over Fields
• \(SK_1\)-like functors for division algebras
• Free subgroups in maximal subgroups of \(\text{GL}_1(D)\)
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