Engel-4 Groups of Exponent 5. II. Orders

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.