some remarks on unipotent automorphisms

An automorphism α of the group g is said to be n-unipotent if [g,n α] = 1 for all g ∈ g. in this paper we obtain some results related to nilpotency of groups of n-unipotent automorphisms of solvable groups. we also show that, assuming the truth of a conjecture about the representation theory of solvable groups raised by p. neumann, it is possible to produce, for a suitable prime p, an example of a f.g. solvable group possessing a group of p-unipotent automorphisms which is isomorphic to an infinite burnside group. conversely we show that, if there exists a f.g. solvable group g with a non nilpotent p-group h of n-automorphisms, then there is such a counterexample where n is a prime power and h has finite exponent.