Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T07:59:43.767Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)