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ENGEL-4 GROUPS OF EXPONENT 5. II. ORDERS

Published online by Cambridge University Press:  01 September 1999

M. F. NEWMAN  and
MICHAEL VAUGHAN-LEE
M. F. NEWMAN
Affiliation:
School of Mathematical Sciences, Australian National University, ACT 0200, Australia. newman@maths.anu.edu.au
MICHAEL VAUGHAN-LEE
Affiliation:
Christ Church, Oxford, OX1 1DP. vlee@maths.ox.ac.uk
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Abstract

Engel-4 groups of exponent 5 are now known to be locally finite. In this paper we determine the orders of the largest finite groups of this kind on $m$ generators.

In the process we show that such a group has a subdirect decomposition into a group which is centre-by-Engel-3 and one which is nilpotent of class at most 10. We work via associated Lie algebras and Lie superalgebras and make use of computer calculations.

1991 Mathematics Subject Classification: 20F45.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 2 , September 1999 , pp. 283 - 317
Copyright
1999 London Mathematical Society

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