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A Characterization of Finite Soluble Groups by Laws in Two Variables

A Characterization of Finite Soluble Groups by Laws in Two Variables Abstract Define a sequence (sn) of two-variable words in variables x, y as follows: s0(x, y) = x, sn+1(x,y)=[sn(x, y]−y, sn(x,y) for n ≥ 0. It is shown that a finite group G is soluble if and only if sn is a law of G for all but finitely many values of n. 2000 Mathematics Subject Classification 20D10, 20D06. © London Mathematical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

A Characterization of Finite Soluble Groups by Laws in Two Variables

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References (8)

Publisher
Oxford University Press
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609304003959
Publisher site
See Article on Publisher Site

Abstract

Abstract Define a sequence (sn) of two-variable words in variables x, y as follows: s0(x, y) = x, sn+1(x,y)=[sn(x, y]−y, sn(x,y) for n ≥ 0. It is shown that a finite group G is soluble if and only if sn is a law of G for all but finitely many values of n. 2000 Mathematics Subject Classification 20D10, 20D06. © London Mathematical Society

Journal

Bulletin of the London Mathematical Society – Oxford University Press

Published: Apr 1, 2005

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