On the existence of normal maximal subgroups in division rings

DOI10.1016/S0022-4049(01)00175-XzbMath1006.16018MaRDI QIDQ1612114

M. Mahdavi-Hezavehi, Saieed Akbari

Publication date: 22 August 2002

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

maximal subgroupsBrauer groupssubgroups of finite indexcentral division algebrasmultiplicative groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) Infinite-dimensional and general division rings (16K40) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60) Skew fields, division rings (12E15)

Related Items (9)

Nontriviality of certain quotients of \(K_1\) groups of division algebras. ⋮ Division Algebras with Radicable Multiplicative Groups ⋮ A Criterion for the Triviality ofG(D) and Its Applications to the Multiplicative Structure ofD ⋮ Nilpotent maximal subgroups of \(\text{GL}_n(D)\). ⋮ On the non-triviality of \(G(D)\) and the existence of maximal subgroups of \(\text{GL}_1(D)\). ⋮ UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS ⋮ On maximal subgroups of the multiplicative group of a division algebra. ⋮ A Decomposition Theorem for CK₁of Central Simple Algebras ⋮ Maximal subgroups of \(\text{GL}_n(D)\)

Cites Work

• Maximal subgroups of \(\text{GL}_1(D)\)
• Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central
• Extending valuations to algebraic division algebras
• Normal subgroups of $GL_n(D)$ are not finitely generated
• Multiplicative Groups of Fields
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