The soluble subgroups and the Tits alternative in linear groups over rings of fractions of polycyclic group rings. I

DOI10.1016/0022-4049(93)90105-3zbMath0784.20025OpenAlexW2072043843MaRDI QIDQ1210356

A. I. Lichtman

Publication date: 8 August 1993

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(93)90105-3

zbMATH Keywords

Krull dimensioncrossed productdivision ringsTits alternativederived lengthsoluble subgroupsHirsch numberdivision rings of quotientsGoldie \(F\)-algebragroup algebras of torsion-free polycyclic-by-finite groupssubrings of matrix ring

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Infinite-dimensional and general division rings (16K40) Nilpotent groups (20F18) Other matrix groups over rings (20H25) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Linear algebraic groups over adèles and other rings and schemes (20G35)

Cites Work

• On Artin's conjecture
• Dimensions of division rings
• Free subgroups in linear groups over some skew fields
• Artin's conjecture for primitive roots
• On PI-subrings of matrix rings over some classes of skew fields
• On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group
• On embedding of group rings in division rings
• Transcendental division algebras and simple Noetherian rings
• On the semisimplicity of group rings of some locally finite groups
• Group rings of polycyclic groups
• Strong finiteness conditions in locally finite groups
• Free subgroups in linear groups
• Applications of a New K-Theoretic Theorem to Soluble Group Rings
• Primitivity in representations of polycyclic groups
• Universal fields of fractions for polycyclic group algebras
• Trace Functions in the Ring of Fractions of Polycyclic Group Rings
• On Subgroups of the Multiplicative Group of Skew Fields
• Observations on group rings
• Finitely Generated Groups (mod p)
• On Embedding of Group Rings of Residually Torsion Free Nilpotent Groups into Skew Fields
• Finite Dimensional Subalgebras in Matrix Rings Over Transcendental Division Algebras
• The Logarithmic Limit-Set of an Algebraic Variety
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