FRATTINI SUBGROUP OF THE UNIT GROUP OF CENTRAL SIMPLE ALGEBRAS

DOI10.1142/S0219498812500612zbMath1253.20053OpenAlexW2107378139MaRDI QIDQ2893001

H. R. Dorbidi, M. Mahdavi-Hezavehi

Publication date: 25 June 2012

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

Full work available at URL: https://doi.org/10.1142/s0219498812500612

zbMATH Keywords

Frattini subgroupgeneral linear groups over division rings

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)

Cites Work

• On maximal subgroups of the multiplicative group of a division algebra.
• Maximal subgroups of \(\text{GL}_1(D)\)
• Tits alternative for maximal subgroups of \(\text{GL}_n(D)\).
• Maximal subgroups of \(\text{GL}_n(D)\)
• Nilpotent maximal subgroups of \(\text{GL}_n(D)\).
• UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS
• A Note on Subnormal Subgroups of Division Algebras
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
• Free subgroups in maximal subgroups of \(\text{GL}_1(D)\)
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