On normal subgroups of the unit group of a quaternion algebra over a Pythagorean field

DOI10.1007/s41980-019-00254-yzbMath1452.16036OpenAlexW2951417208WikidataQ114217378 ScholiaQ114217378MaRDI QIDQ2287037

Mohammad Gholamzadeh Mahmoudi

Publication date: 23 January 2020

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41980-019-00254-y

zbMATH Keywords

orthogonal groupFrobenius normrotation groupquaternion algebraPythagorean fieldCayley parametrizationnon-Archimedean ordering

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Finite-dimensional division rings (16K20) Classical groups (11E57) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Units, groups of units (associative rings and algebras) (16U60)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Anisotropic groups of type \(A_n\) and the commuting graph of finite simple groups.
• On derived groups of normal simple algebra
• Subnormal subgroups of p-adic division algebras
• Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups
• The finite quotients of the multiplicative group of a division algebra of degree \(3\) are solvable
• On the multiplicative group of simple algebras and orthogonal groups of three dimensions
• Existence of Nonabelian Free Subgroups in the Maximal Subgroups of GL_n(D)
• Conjugates in Division Rings
• A Note on Subnormal Subgroups of Division Algebras
• Zur orthogonalen Geometrie über pythagoreischen Körpern.
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
• On the Structure of Local Orthogonal Groups
• The Norm 1 Group of -Adic Division Algebra
• Les déterminants sur un corps non commutatif