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; H. SMITH, H.; J., Wiegold. - In: ILLINOIS JOURNAL OF MATHEMATICS. - ISSN 0019-2082. - STAMPA. - 47:1(2003), pp. 141-156.
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
