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Paper   IPM / M / 773
School of Mathematics
  Title:   Certain locally nilpotent varieties of groups
  Author(s):  A. Abdollahi
  Status:   Published
  Journal: Bull. Aust. Math. Soc.
  Vol.:  67
  Year:  2003
  Pages:   115-119
  Supported by:  IPM
Let c ≥ 0, d ≥ 2 be integers and Nc(d) be the variety of groups in which every d-generator 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 Nc(d) is locally nilpotent? We prove that if c ≤ 2d+2d−1−3 then the variety Nc(d) is locally nilpotent and we reduce the question of Gupta about the periodic groups in Nc(d) to the prime power finite exponent groups in this variety.

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