On matrix rings and linear groups over fields of fractions of group rings and enveloping algebras. II

DOI10.1016/0021-8693(84)90187-XzbMath0544.16010MaRDI QIDQ796613

A. I. Lichtman

Publication date: 1984

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

zbMATH Keywords

Jacobson radicalgroup ringmatrix ringJordan functiondivision ring of fractionsfinitely generated subringnoncentral normal subgroupnoncyclic free subgroupsolvable residually torsion free nilpotent groupsum of nilpotent elementsOre domainperiodic subgroupsolvable-by- finite torsion free group

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Universal enveloping (super)algebras (17B35) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Nilpotent groups (20F18) Other matrix groups over rings (20H25) Local properties of groups (20E25) Localization and associative Noetherian rings (16P50) Division rings and semisimple Artin rings (16Kxx)

Related Items

Free subgroups in linear groups over some skew fields, A Survey on Free Objects in Division Rings and in Division Rings with an Involution, FREE GROUP ALGEBRAS IN DIVISION RINGS, On Embedding of Group Rings of Residually Torsion Free Nilpotent Groups into Skew Fields, Obtaining free group algebras in division rings generated by group graded rings, Computing the inversion height of some embeddings of the free algebra and the free group algebra., Free group algebras in division rings with valuation I, Free symmetric group algebras in division rings generated by poly-orderable groups., Free Structures in Division Rings, Free group algebras in the field of fractions of differential polynomial rings and enveloping algebras, Free subgroups in \(k(x_{1},\ldots,x_{n})(X;\sigma)\) and \(k(x,y)(X;\sigma)\), Growth in enveloping algebras, The inversion height of the free field is infinite.

Cites Work

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• On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group
• On linear groups over a field of fractions of a polycyclic group ring
• A note on curvature and fundamental group
• Growth of finitely generated solvable groups
• The structure of several classes of matrix groups over a division ring
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• The Residual Nilpotence of Wreath Products
• Invariant Measures and Growth Conditions