Maximal subgroups of \(\text{GL}_1(D)\)

DOI10.1006/jabr.1998.7792zbMath0933.16033OpenAlexW2592875436MaRDI QIDQ1305003

Mohammad Gholamzadeh Mahmoudi, M. Mahdavi-Hezavehi, Saieed Akbari

Publication date: 25 January 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7792

zbMATH Keywords

maximal subgroupsmultiplicative groupsAbelian maximal subgroupsfinitely generated normal subgroupsfinite dimensional division algebraslocally finite-dimensional algebrassoluble maximal subgroups

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Maximal subgroups (20E28) Infinite-dimensional and general division rings (16K40) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (24)

Subgroups ofGL₁(R) for Local RingsR ⋮ Subnormal subgroups of the groups of rational points of reductive algebraic groups ⋮ FRATTINI SUBGROUP OF THE UNIT GROUP OF CENTRAL SIMPLE ALGEBRAS ⋮ A Criterion for the Triviality ofG(D) and Its Applications to the Multiplicative Structure ofD ⋮ Nilpotent maximal subgroups of \(\text{GL}_n(D)\). ⋮ Existence of Nonabelian Free Subgroups in the Maximal Subgroups of GL_n(D) ⋮ On subnormal subgroups in general skew linear groups. ⋮ Maximal subgroups of \(\mathrm{SL}_{n}(D)\) ⋮ Tits alternative for maximal subgroups of \(\text{GL}_n(D)\). ⋮ A note on Lie ideals of prime rings ⋮ Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central ⋮ Polynomial identities and maximal subgroups of skew linear groups. ⋮ Free subgroups in maximal subgroups of \(\text{GL}_1(D)\) ⋮ UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS ⋮ On Locally Nilpotent Subgroups ofGL₁(D) ⋮ Identities on Maximal Subgroups of GL_n(D) ⋮ Free subgroups in maximal subgroups ofGL_n(D) ⋮ Maximal subgroups of \(\text{GL}_n(D)\) with finite conjugacy classes. ⋮ SOLUBLE MAXIMAL SUBGROUPS IN GL_n(D) ⋮ On maximal subgroups of the multiplicative group of a division algebra. ⋮ Some notes on Lie ideals in division rings ⋮ Maximal subgroups of \(\text{GL}_n(D)\) ⋮ On the existence of normal maximal subgroups in division rings ⋮ Locally Finite Conditions on Maximal Subgroups of GL_n(D)

Cites Work

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• Multiplicative commutators in division rings
• On additive commutator groups in division rings
• Free subgroups in linear groups
• 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
• Soluble subgroups of the multiplicative group of a field

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