Irreducible Subgroups of GL 1(D) Satisfying Group Identities

DOI10.1081/AGB-200058549zbMath1109.16015OpenAlexW2061463009MaRDI QIDQ5704521

M. Mahdavi-Hezavehi, R. Ebrahimian, Dariush Kiani

Publication date: 15 November 2005

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

Full work available at URL: https://doi.org/10.1081/agb-200058549

zbMATH Keywords

multiplicative groupsfinite dimensional central division algebrasmaximal subfieldsirreducible subgroupsgroup identities

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Other matrix groups over rings (20H25) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60) Skew fields, division rings (12E15)

Related Items (4)

Polynomial identities and maximal subgroups of skew linear groups. ⋮ Crossed product conditions for division algebras of prime power degree. ⋮ Maximal subgroups of \(\text{GL}_n(D)\) with finite conjugacy classes. ⋮ On soluble-by-finite subgroups of division algebras.

Cites Work

• Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central
• Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
• Cyclicity conditions for division algebras of prime degree
• Free subgroups in maximal subgroups of \(\text{GL}_1(D)\)
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