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.
Citation
Giovanni Cutolo. Howard Smith. James Wiegold. "$p$-groups of maximal class as automorphism groups." Illinois J. Math. 47 (1-2) 141 - 156, Spring/Summer 2003. https://doi.org/10.1215/ijm/1258488144
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