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Finite Axiomatization of Finite Soluble Groups
Author(s) -
Wilson John S.
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706023106
Subject(s) - mathematics , conjugate , order (exchange) , sentence , product (mathematics) , finite group , group (periodic table) , pure mathematics , finite element method , algebra over a field , computer science , physics , mathematical analysis , geometry , natural language processing , business , finance , quantum mechanics , thermodynamics
It is proved that the finite soluble groups can be characterized among finite groups by a first‐order sentence, namely, the sentence that asserts that no non‐trivial element g is a product of 56 commutators [ x, y ] with entries x, y conjugate to g .