Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-07T21:36:17.451Z Has data issue: false hasContentIssue false
  • English
  • Français

VARIETIES OF GROUPS OF EXPONENT 4

Published online by Cambridge University Press:  01 December 1999

MARTYN QUICK
MARTYN QUICK
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford OX1 3LB; [email protected]
Get access

Abstract

It is proved that the variety of all 4-Engel groups of exponent 4 is a maximal proper subvariety of the Burnside variety [Bfr ]4, and the consequences of this are discussed for the finite basis problem for varieties of groups of exponent 4. It is proved that, for r [ges ] 2, the 4-Engel verbal subgroup of the r-generator Burnside group B(r, 4) is irreducible as an [ ]2GL(r, 2)-module. It is observed that the variety of all 4-Engel groups of exponent 4 is insoluble, but not minimal insoluble.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 747 - 756
Copyright
The London Mathematical Society 1999

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.)