Two-variable identities for finite solvable groups.

DOI10.1016/j.crma.2003.09.003zbMath1047.20014OpenAlexW2086808249MaRDI QIDQ1420139

D. Massart

Publication date: 28 January 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2003.09.003

zbMATH Keywords

finite solvable groupsrational pointsprosolvable groupsalgebraic varietieslawsfinite varietiesLang-Weil estimates

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Rational points (14G05) Finite ground fields in algebraic geometry (14G15) Finite simple groups and their classification (20D05) Quasivarieties and varieties of groups (20E10) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Engel conditions (20F45)

Related Items (9)

Reducibility vs. definability for pseudovarieties of semigroups ⋮ On the number of conjugates defining the solvable radical of a finite group. ⋮ Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics. ⋮ BURNSIDE-TYPE PROBLEMS RELATED TO SOLVABILITY ⋮ A description of Baer-Suzuki type of the solvable radical of a finite group. ⋮ Geometry and arithmetic of verbal dynamical systems on simple groups (with an appendix by Nathan Jones) ⋮ Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups ⋮ Thompson-like characterizations of the solvable radical. ⋮ CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL

Uses Software

• SINGULAR

Cites Work

• Characterization of finite soluble groups by laws in a small number of variables
• Zur Theorie der untergruppenabgeschlossenen Formationen: Endliche Varietäten
• Rigid geometry, Lefschetz-Verdier trace formula and Deligne's conjecture
• Two-variable identities in groups and Lie algebras.
• Dynamics of implicit operations and tameness of pseudovarieties of groups
• Nonsolvable finite groups all of whose local subgroups are solvable
• Generalized soluble and generalized nilpotent groups
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