Abstract
The question of whether a group of automorphisms $A$ containing the inner automorphisms of a nonabelian $p$-group $G$ can generate a local endomorphism near-ring when $A$ is not a $p$-group is considered. Conditions on $A$ are obtained which give us that the endomorphism near-ring generated by $A$ is not local. An example is given showing that the endomorphism near-ring generated by $A$ can be local when these conditions are not met.
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