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A CHARACTERIZATION OF FINITE SOLUBLE GROUPS BY LAWS IN TWO VARIABLES

Published online by Cambridge University Press:  10 March 2005

JOHN N. BRAY ,
JOHN S. WILSON  and
ROBERT A. WILSON
JOHN N. BRAY
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Rd, London E1 4NS, United [email protected], [email protected]
JOHN S. WILSON
Affiliation:
Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, United [email protected]
ROBERT A. WILSON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Rd, London E1 4NS, United [email protected], [email protected]
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Abstract

Define a sequence $(s_{n})$ of two-variable words in variables $x$, $y$ as follows: $s_{0}(x,y)=x$, $s_{n+1}(x,y)=[s_{n}(x,y)^{-y},s_{n}(x,y)]$ for $n\geq0$. It is shown that a finite group $G$ is soluble if and only if $s_{n}$ is a law of $G$ for all but finitely many values of $n$.

Keywords

20D1020D06
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 179 - 186
Copyright
© The London Mathematical Society 2005

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