On groups of exponent four. II

Abstract

C. R. B. Wright has shown that the nilpotency class of an n n -generator group of exponent four is at most 3 n − 1 3n - 1 . This bound is believed to be too large for higher values of n n . In this note it is shown that if for some large enough integer n n this bound can be improved to [ 2 1 2 n ] − 1 [2\tfrac {1}{2}n] - 1 , then the free group of exponent four of infinite rank is solvable.