This paper deals with an old problem: are there nontrivial finite p-groups which are isomorphic to their full automorphism group, besides the dihedral group of order 8? The answer (in the negative) is obtained in some special cases, including groups of class 2, powerful groups, groups with centre of prime order or an abelian subgroup of prime index, class-3 groups with cyclic centre, groups with coclass at most 3 and others.
On a question about automorphisms of finite p-groups / Cutolo, Giovanni. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 9:2(2006), pp. 231-250. [10.1515/JGT.2006.016]
On a question about automorphisms of finite p-groups
CUTOLO, GIOVANNI
2006
Abstract
This paper deals with an old problem: are there nontrivial finite p-groups which are isomorphic to their full automorphism group, besides the dihedral group of order 8? The answer (in the negative) is obtained in some special cases, including groups of class 2, powerful groups, groups with centre of prime order or an abelian subgroup of prime index, class-3 groups with cyclic centre, groups with coclass at most 3 and others.File in questo prodotto:
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