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On groups of exponent four. II


Authors: C. K. Gupta and N. D. Gupta
Journal: Proc. Amer. Math. Soc. 31 (1972), 360-362
MSC: Primary 20.27
DOI: https://doi.org/10.1090/S0002-9939-1972-0289631-2
MathSciNet review: 0289631
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Abstract: C. R. B. Wright has shown that the nilpotency class of an $ n$-generator group of exponent four is at most $ 3n - 1$. This bound is believed to be too large for higher values of $ n$. In this note it is shown that if for some large enough integer $ n$ this bound can be improved to $ [2\tfrac{1}{2}n] - 1$, then the free group of exponent four of infinite rank is solvable.


References [Enhancements On Off] (What's this?)

  • [1] Narain D. Gupta and Seán J. Tobin, On certain groups with exponent four, Math. Z. 102 (1967), 216-226. MR 36 #5220. MR 0222168 (36:5220)
  • [2] Narain D. Gupta and Kenneth W. Weston, On groups of exponent four, J. Algebra 17 (1971), 59-66. MR 0268277 (42:3176)
  • [3] C. R. B. Wright, On the nilpotency class of a group of exponent four, Pacific J. Math. 11 (1961), 387-394. MR 23 #A927. MR 0123602 (23:A927)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289631-2
Keywords: Exponent four, nilpotency class, solvability, commutator, verbal closure, free group, variety
Article copyright: © Copyright 1972 American Mathematical Society

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