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.

p-groups of maximal class as automorphism groups.

CUTOLO, GIOVANNI;
2003

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/3866
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