Free subgroups of division algebras

DOI10.1080/00927879508825339zbMath0833.16015OpenAlexW2008473651MaRDI QIDQ4834904

Nikolaus Vonessen, Zinovy Reichstein

Publication date: 11 March 1996

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

Full work available at URL: https://doi.org/10.1080/00927879508825339

zbMATH Keywords

free groupsmultiplicative groupsskew fieldsuncountable center

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Infinite-dimensional and general division rings (16K40) Conditions on elements (16U99) Units, groups of units (associative rings and algebras) (16U60)

Related Items (10)

Free algebras and free groups in Ore extensions and free group algebras in division rings. ⋮ A note on the existence of non-cyclic free subgroups in division rings. ⋮ Free subgroups in almost subnormal subgroups of general skew linear groups ⋮ Generalized power central group identities in almost subnormal subgroups of $\operatorname {GL}_n(D)$ ⋮ Free \(^*\)-subalgebras of C\(^*\)-algebras ⋮ Free subalgebras of division algebras over uncountable fields. ⋮ FREE SYMMETRIC AND UNITARY PAIRS IN DIVISION RINGS WITH INVOLUTION ⋮ Free group algebras in the field of fractions of differential polynomial rings and enveloping algebras ⋮ A Note on Free Groups in the Ring of Fractions of Skew Polynomial Rings ⋮ Makar-Limanov's conjecture on free subalgebras.

Cites Work

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• Are there free groups in division rings?
• Rational identities and applications to algebra and geometry
• Words Periodic over the Center of a Division Ring
• Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
• Polynomial Rings Over Goldie Rings are Often Goldie
• On Subgroups of the Multiplicative Group of Skew Fields

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