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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]
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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

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