Certain locally nilpotent varieties of groups

Abstract

Let c ≥ 0, d ≥ 2 be integers and be the variety of groups in which every d -generator subgroup is nilpotent of class at most c . N.D. Gupta asked for what values of c and d is it true that is locally nilpotent? We prove that if c ≤ 2 d + 2 d −1 − 3 then the variety is locally nilpotent and we reduce the question of Gupta about the periodic groups in to the prime power exponent groups in this variety.