Invariable generation of infinite groups.

DOI10.1016/j.jalgebra.2014.08.030zbMath1318.20032arXiv1407.4631OpenAlexW2151340275WikidataQ101241181 ScholiaQ101241181MaRDI QIDQ468705

Alexander Lubotzky, Aner Shalev, William M. Kantor

Publication date: 7 November 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4631

zbMATH Keywords

profinite completionsprofinite groupslinear groupscongruence subgroup propertyinvariable generation

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Generators, relations, and presentations of groups (20F05) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Linear algebraic groups over global fields and their integers (20G30) Limits, profinite groups (20E18) Probabilistic methods in group theory (20P05)

Related Items

Invariable generation of prosoluble groups. ⋮ Sliceable groups and towers of fields ⋮ Invariable generation of iterated wreath products of cyclic groups ⋮ A few remarks on invariable generation in infinite groups ⋮ Invariable generation and the Houghton groups ⋮ Invariable generation does not pass to finite index subgroups ⋮ Topological generation of special linear groups ⋮ Invariable generation and wreath products ⋮ Handlebody subgroups in a mapping class group ⋮ Invariable generation of certain groups of piecewise linear homeomorphisms of the interval ⋮ Invariable generation of Thompson groups ⋮ Invariable generation of finite classical groups ⋮ Some examples of invariably generated groups ⋮ Minimal invariable generating sets

Cites Work

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• Invariable generation and the Chebotarev invariant of a finite group.
• Groups of bounded period with subgroups of prime order
• Small cancellations over relatively hyperbolic groups and embedding theorems.
• Strong approximation for Zariski-dense subgroups of semi-simple algebraic groups
• On Burnside's problem on periodic groups
• Maximal subgroups of infinite index in finitely generated linear groups
• Random sets which invariably generate the symmetric group
• Transitive groups with fixed-point free permutations
• Transitive groups with fixed-point-free permutations. II
• Strong approximation for Zariski dense subgroups over arbitrary global fields
• Subgroup growth.
• Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks.
• Subgroup growth and congruence subgroups
• Alternating quotients of Fuchsian groups
• Groups covered by conjugates of proper subgroups.
• The probability of generating a finite classical group
• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements
• Simple groups admit Beauville structures
• Endomorphisms of linear algebraic groups
• Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem
• Embedding Theorems for Groups
• Finiteness Conditions for Soluble Groups