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Proceedings of the American Mathematical Society

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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
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.


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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