Abstract
If G is a finite group and [Formula: see text] is a group of automorphisms of G, then it is known that the matrix near-ring [Formula: see text] is a subnear-ring of the centralizer near-ring [Formula: see text] for every m ≥ 2. Conditions are known under which [Formula: see text] is a proper subnear-ring of [Formula: see text], and if [Formula: see text] and G are abelian, then conditions are known which imply the equality [Formula: see text]. In this paper, we characterize the groups [Formula: see text] of automorphisms of a cyclic p-group G for which this equality holds. We also show that for every group [Formula: see text] of automorphisms of a cyclic p-group G, either all the nonzero orbits of G are of unique type or none of the orbits of G is of unique type if p is odd, and there is a third possibility if p=2, namely precisely one of the orbits of G is of unique type.
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