Nonabelian free subgroups in homomorphic images of valued quaternion division algebras

DOI10.1090/S0002-9939-06-08385-7zbMath1117.16007WikidataQ123222235 ScholiaQ123222235MaRDI QIDQ3419884

Yoav Segev, Andrei S. Rapinchuk, Louis Halle Rowen

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Whitehead groupsvaluationsmultiplicative groupsquaternion division algebraspure quaternionsresidue algebras

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Grothendieck groups, (K)-theory, etc. (16E20) Finite-dimensional division rings (16K20) Classical groups (11E57) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Units, groups of units (associative rings and algebras) (16U60) Valued fields (12J10) Stability for linear groups (19B14)

Related Items (1)

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

Cites Work

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• Normal subgroups generated by a single pure element in quaternion algebras.
• Free subgroups in linear groups
• On the Multiplicative Group of a Division Ring
• Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable

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