Explicit free groups in division rings

DOI10.1090/S0002-9939-2014-12230-1zbMath1317.16013MaRDI QIDQ5496290

Jairo Z. Goncalves, Donald S.Passman

Publication date: 30 January 2015

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

zbMATH Keywords

skew fields of fractionsfree subgroupsfree groupscommutatorsdivision ringsmultiplicative groupsnilpotent torsion-free groupscentre of division ringsLichtman conjecturesecond centre of nilpotent groups

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Infinite-dimensional and general division rings (16K40) Free nonabelian groups (20E05) Units, groups of units (associative rings and algebras) (16U60)

Related Items (6)

Free algebras and free groups in Ore extensions and free group algebras in division rings. ⋮ Free symmetric and unitary pairs in the field of fractions of torsion-free nilpotent group algebras ⋮ Free unit groups in group rings and division rings: My collaboration with Don Passman ⋮ Free pairs of symmetric and unitary units in normal subgroups of a division ring ⋮ Free groups in normal subgroups of the multiplicative group of a division ring. ⋮ Free pairs of symmetric elements in normal subgroups of division rings

Cites Work

• On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group
• Free products of units in algebras. I: Quaternion algebras
• Free products of units in algebras. II: Crossed products
• A Survey on Free Objects in Division Rings and in Division Rings with an Involution
• On Subgroups of the Multiplicative Group of Skew Fields
• Free Subgroups of Normal Subgroups of the Multiplicative Group of Skew Fields
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