THE NILPOTENCY CLASS OF FINITE GROUPS OF EXPONENT p
نویسنده
چکیده
We investigate the properties of Lie algebras of characteristic p which satisfy the Engel identity xy" = 0 for some n < p. We establish a criterion which (when satisfied) implies that if a and b are elements of an Engel-n Lie algebra L then abn~2 generates a nilpotent ideal of I. We show that this criterion is satisfied for n = 6, p = 1, and we deduce that if G is a finite m-generator group of exponent 7 then G is nilpotent of class at most 51m8 .
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