UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS

DOI10.1142/S0219498810004300zbMath1215.16030OpenAlexW1965574926MaRDI QIDQ3069769

R. Fallah-Moghaddam, M. Mahdavi-Hezavehi

Publication date: 19 January 2011

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498810004300

zbMATH Keywords

general linear groupsmaximal subgroupsdivision ringsFrattini subgroupskew linear groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) Other matrix groups over rings (20H25) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (4)

FRATTINI SUBGROUP OF THE UNIT GROUP OF CENTRAL SIMPLE ALGEBRAS ⋮ Maximal subgroups of \(\mathrm{SL}_{n}(D)\) ⋮ Free subgroups in maximal subgroups of SLn(D) ⋮ Free subgroups in maximal subgroups ofGL_n(D)

Cites Work

• On maximal subgroups of the multiplicative group of a division algebra.
• Maximal subgroups of \(\text{GL}_1(D)\)
• On the existence of normal maximal subgroups in division rings
• On the non-triviality of \(G(D)\) and the existence of maximal subgroups of \(\text{GL}_1(D)\).
• A Note on Subnormal Subgroups of Division Algebras
• Triviality of the Functor Coker(K ₁(F) → K ₁(D)) for Division Algebras
• Free subgroups in maximal subgroups of \(\text{GL}_1(D)\)

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