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2006•Journal of Group TheoryRequires access

On a question about automorphisms of finite p-groups

Giovanni Cutolo

Open publisher page 6 citations

Abstract

This paper deals with an old problem: are there non-trivial 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.

About this research paper

What this paper is about

This paper deals with an old problem: are there non-trivial 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.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper deals with an old problem: are there non-trivial 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.

Key concepts: Mathematics, Dihedral group, Automorphism, p-group, Prime (order theory), Non-abelian group, Abelian group, Order (exchange)

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