FREE SYMMETRIC AND UNITARY PAIRS IN DIVISION RINGS WITH INVOLUTION

DOI10.1142/S0218196705002177zbMath1088.16022OpenAlexW2105880060MaRDI QIDQ4680579

Vitor O. Ferreira, Arnaldo Mandel, Jairo Z. Goncalves

Publication date: 7 June 2005

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196705002177

zbMATH Keywords

free subgroupsinvolutionssymmetric elementsdivision ringsmultiplicative groupsTits alternativeunitary elements

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Infinite-dimensional and general division rings (16K40) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Free nonabelian groups (20E05) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (13)

Free algebras and free groups in Ore extensions and free group algebras in division rings. ⋮ A Survey on Free Objects in Division Rings and in Division Rings with an Involution ⋮ Free symmetric and unitary pairs in group algebras with involution ⋮ Obtaining free group algebras in division rings generated by group graded rings ⋮ Symmetric units satisfying a group identity. ⋮ Free symmetric and unitary pairs in division rings infinite-dimensional over their centers. ⋮ Free unit groups in group rings and division rings: My collaboration with Don Passman ⋮ Free symmetric pairs in the field of fractions of enveloping Lie algebras with involution ⋮ *-Group identities on units of division rings ⋮ 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. ⋮ Unitary Units Satisfying a Group Identity ⋮ Makar-Limanov's conjecture on free subalgebras.

Cites Work

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• Construction of free subgroups in the group of units of modular group algebras
• Free subgroups of division algebras
• Unitary units in group algebras

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