The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups.

DOI10.1007/s00209-005-0854-1zbMath1101.20027OpenAlexW1988737396WikidataQ123294101 ScholiaQ123294101MaRDI QIDQ811844

Andrei S. Rapinchuk

Publication date: 23 January 2006

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-005-0854-1

zbMATH Keywords

finite simple groupsglobal fieldsfinite dimensional central division algebrasanisotropic groupscommuting graphs of finite groupssimple simply connected algebraic groups

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Linear algebraic groups over global fields and their integers (20G30) Finite simple groups and their classification (20D05) Finite-dimensional division rings (16K20) Classical groups (11E57) Units, groups of units (associative rings and algebras) (16U60)

Related Items (3)

On the congruence kernel for simple algebraic groups ⋮ Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity ⋮ On graphs and valuations.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Anisotropic groups of type \(A_n\) and the commuting graph of finite simple groups.
• Some applications of the first cohomology group
• On the group of norm 1 elements in a division algebra
• Finiteness of quotient groups of discrete subgroups
• Strong approximation for semi-simple groups over function fields
• On finite homomorphic images of the multiplicative group of a division algebra
• Generation of classical groups
• Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups
• Subgroup growth.
• The probability of generating a finite simple group
• On Conjugates in Division Rings
• Multiplicative Subgroups of Finite Index in a Ring
• Some applications of Wedderburn's factorisation theorem
• Multiplicative Subgroups of Finite Index in a Division Ring
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
• The Norm 1 Group of -Adic Division Algebra
• Valuation-like maps and the congruence subgroup property
• The commuting graph of minimal nonsolvable groups

This page was built for publication: The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups.