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G. Cutolo, H. Smith and J. Wiegold
p-groups of maximal class as automorphism groups
Illinois J. Math., 47, (2003), pp. 141–156.
MathSciNet Zentralblatt Comments Abstract Full Text
Abstract
We classify the (finite) p-groups of maximal class that are isomorphic to the full automorphism group of a (finite or infinite) group. The only such p-groups are the nonabelian groups of order 8 and 3-groups in a certain family, whose structure is fully described. Up to isomorphism there is exactly one such 3-group for each even nilpotency class greater than 2, and none for other classes.
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