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ABSTRACT
Let G be a finite group admitting an automorphism such that
. If
has prime order q then, by well-known results of Higman and Thompson, G is nilpotent of class bounded by some function
depending on q alone. We extend this in the following way. Assume that
is of square-free order n , prime to the order of G . Suppose that there exists a positive integer m such that
for any non-trivial
. Then G is nilpotent and the nilpotency class of G is bounded by some function depending only on m and n .
ACKNOWLEDGMENT
The first author was supported by CNPq-Brazil.