Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central

DOI10.1006/jabr.1999.8096zbMath0947.20032OpenAlexW1985694013MaRDI QIDQ1972410

S. Yasamin, M. Mahdavi-Hezavehi, Mohammad Gholamzadeh Mahmoudi

Publication date: 7 June 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8096

zbMATH Keywords

finite-dimensional division algebrasmultiplicative groupsfinitely generated subnormal subgroups

Mathematics Subject Classification ID

Chains and lattices of subgroups, subnormal subgroups (20E15) Other matrix groups over rings (20H25) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (16)

Subgroups ofGL₁(R) for Local RingsR ⋮ Subnormal subgroups of the groups of rational points of reductive algebraic groups ⋮ A note on skew linear groups of finite rank ⋮ On subnormal subgroups in general skew linear groups. ⋮ Nilpotent and polycyclic-by-finite maximal subgroups of skew linear groups. ⋮ Free subgroups in almost subnormal subgroups of general skew linear groups ⋮ Tits alternative for maximal subgroups of \(\text{GL}_n(D)\). ⋮ Irreducible Subgroups of GL ₁(D) Satisfying Group Identities ⋮ On weakly locally finite division rings ⋮ Tits Alternative for Maximal Subgroups of Skew Linear Groups ⋮ Free subgroups in maximal subgroups of \(\text{GL}_1(D)\) ⋮ Identities on Maximal Subgroups of GL_n(D) ⋮ Maximal Subgroups of Subnormal Subgroups ofGL_n(D) with Finite Conjugacy Classes ⋮ Locally solvable and solvable-by-finite maximal subgroups of \(\mathrm{GL}_n (D)\) ⋮ Some notes on Lie ideals in division rings ⋮ On the existence of normal maximal subgroups in division rings

Cites Work

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• Maximal subgroups of \(\text{GL}_1(D)\)
• Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
• Extension of valuations on derived groups of division rings
• On derived groups of division rings II
• Normal subgroups of $GL_n(D)$ are not finitely generated

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