Normal subgroups generated by a single pure element in quaternion algebras.

DOI10.1016/j.jalgebra.2005.11.015zbMath1119.16018OpenAlexW2078270681MaRDI QIDQ854893

Yoav Segev, Louis Halle Rowen

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.11.015

zbMATH Keywords

Whitehead groupsmultiplicative groups of division ringsnormal seriesabsolutely simple algebraic groupsquaternion division algebraspure quaternions

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Derived series, central series, and generalizations for groups (20F14) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60) Stability for linear groups (19B14)

Related Items (2)

An Azumaya Algebra Version of the Kneser–Tits Problem for Groups of TypeD₄ ⋮ Nonabelian free subgroups in homomorphic images of valued quaternion division algebras

Cites Work

• On finite homomorphic images of the multiplicative group of a division algebra
• Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups
• Nonabelian free subgroups in homomorphic images of valued quaternion division algebras
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
• The classification of the finite simple groups
• Intersections of primary powers of a group
• Valuation-like maps and the congruence subgroup property
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