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Let be a prime integer and let
be a free metabelian group of rank
In the paper an automorphism
of order
permuting cyclically fixed bases of
is studied. The subgroup of fixed points of
and the properties of action of
on the commutator subgroup of
are described. There are also given some results concerning such automorphisms of free abelian groups of rank
The authors thank Olga Macedon´ska and Jan Krempa for their helpful comments.
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