BOUNDED GENERATION AND LINEAR GROUPS

DOI10.1142/S0218196703001493zbMath1059.20048MaRDI QIDQ3043515

László Pyber, Miklós Abért, Alexander Lubotzky

Publication date: 6 August 2004

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

zbMATH Keywords

subgroups of finite indexprofinite completionsprofinite groupsgroups of bounded generationproducts of cyclic subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Extensions, wreath products, and other compositions of groups (20E22) Products of subgroups of abstract finite groups (20D40) Other matrix groups over fields (20H20) Limits, profinite groups (20E18)

Related Items

A product decomposition of infinite symmetric groups, Bounded generation of \(S\)-arithmetic subgroups of isotropic orthogonal groups over number fields., On bounded elementary generation for \(\mathrm{SL}_n\) over polynomial rings, Elementary bounded generation for SLn${\rm SL}_n$ for global function fields and n⩾3$n\geqslant 3$, Bounded generation and commutator width of Chevalley groups: function case, Finitely generated groups with polynomial index growth, Ranks of subgroups in boundedly generated groups, Generating Adjoint Groups, Non-virtually abelian anisotropic linear groups are not boundedly generated

Cites Work

• Unnamed Item
• Products of powers in finite simple groups
• Finitely generated groups of polynomial subgroup growth
• On a question of M. Newman on the number of commutators
• Groups of integral representation type
• An application of connectivity theory in graphs to factorizations of elements in groups
• On groups of polynomial subgroup growth
• Compact subgroups of linear algebraic groups
• On \(SS\)-rigid groups and A. Weil's criterion for local rigidity. I
• Nonarithmetic superrigid groups: Counterexamples to Platonov's conjecture
• Strong approximation for Zariski dense subgroups over arbitrary global fields
• Subgroup growth and congruence subgroups
• Closed Subgroups of Profinite Groups
• The finite images of finitely generated groups
• Bounded Elementary Generation of SL n (O)
• BOUNDED GENERATION AND SUBGROUP GROWTH
• BOUNDED GENERATION OF CHEVALLEY GROUPS OVER RINGS OF ALGEBRAICS-INTEGERS
• A note on powers in simple groups
• On Simple Pseudofinite Groups