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Paper IPM / M / 773  


Abstract:  
Let c ≥ 0, d ≥ 2 be integers and N_{c}^{(d)} be the
variety of groups in which every dgenerator subgroup is
nilpotent of class at most c. N.D. Gupta posed this question that
for what values of c and d it is true that N_{c}^{(d)}
is locally nilpotent? We prove that if c ≤ 2^{d}+2^{d−1}−3 then
the variety N_{c}^{(d)} is locally nilpotent and we reduce
the question of Gupta about the periodic groups in
N_{c}^{(d)} to the prime power finite exponent groups in this
variety.
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