Are there free groups in division rings?

DOI10.1007/BF02772670zbMath0597.16017OpenAlexW2049086652MaRDI QIDQ1078641

Arnaldo Mandel, Jairo Z. Goncalves

Publication date: 1986

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02772670

zbMATH Keywords

skew fieldfree subgroupmultiplicative groupnoncentral subnormal subgroupsubstitution mapping

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Units, groups of units (associative rings and algebras) (16U60) Division rings and semisimple Artin rings (16Kxx)

Related Items

Subnormal subgroups in division rings with generalized power central group identities., A Survey on Free Objects in Division Rings and in Division Rings with an Involution, On subnormal subgroups of skew fields, Existence of Nonabelian Free Subgroups in the Maximal Subgroups of GL_n(D), Unnamed Item, Free subgroups of division algebras, Multiplicative subgroups in weakly locally finite 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, Maximal subgroups of \(\mathrm{SL}_{n}(D)\), A NOTE ON SUBNORMAL SUBGROUPS IN DIVISION RINGS CONTAINING SOLVABLE SUBGROUPS, Permutable subgroups in \(\mathrm{GL}_n (D)\) and applications to locally finite group algebras, Free symmetric pairs in the field of fractions of enveloping Lie algebras with involution, Tits alternative for maximal subgroups of \(\text{GL}_n(D)\)., Generalized rational identities of subnormal subgroups of skew fields, Generalized power central group identities in almost subnormal subgroups of $\operatorname {GL}_n(D)$, Tits Alternative for Maximal Subgroups of Skew Linear Groups, Free subgroups in maximal subgroups of \(\text{GL}_1(D)\), Wreath products and subgroups of division rings., Free Subsemigroups of Domains, Algebraic commutators with respect to subnormal subgroups in division rings, Some Skew Linear Groups Satisfying Generalized Group Identities, Free products of units in algebras. I: Quaternion algebras, A commutativity theorem for division rings and an extension of a result of Faith

Cites Work

• Unnamed Item
• Power maps in rings
• Multiplicative commutators in division rings. II
• On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group
• Multiplicative commutators in division rings
• Rational identities and applications to algebra and geometry
• Free subgroups in linear groups
• Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
• Subnormal Subgroups of Division Rings
• On Subgroups of the Multiplicative Group of Skew Fields
• Free Subgroups of Normal Subgroups of the Multiplicative Group of Skew Fields
• A Generalization of the Cartan-Brauer-Hua Theorem