Sequences of words characterizing finite solvable groups.

DOI10.1007/s00605-008-0034-6zbMath1195.20016OpenAlexW2143316058MaRDI QIDQ833316

Evija Ribnere

Publication date: 12 August 2009

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-008-0034-6

zbMATH Keywords

wordsidentitiesGröbner basesfinite simple groupsfinite soluble groupsEngel groupslaws

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) Simple groups: alternating groups and groups of Lie type (20D06) Quasivarieties and varieties of groups (20E10) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Engel conditions (20F45)

Related Items (4)

Iterated identities and iterational depth of groups ⋮ Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics. ⋮ No iterated identities satisfied by all finite groups ⋮ 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
• A CHARACTERIZATION OF FINITE SOLUBLE GROUPS BY LAWS IN TWO VARIABLES
• Identities for finite solvable groups and equations in finite simple groups
• Nonsolvable finite groups all of whose local subgroups are solvable
• Endliche Gruppen I
• On a class of doubly transitive groups
• Sums of Betti numbers in arbitrary characteristic.
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