On automorphism groups of finite \(p\)-groups
type: Item
instance of: scholarly article
title: On automorphism groups of finite \(p\)-groups
zbMATH Open document ID: 0813.20020
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1995-05-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108323
review text: It is proved that, for every odd prime number \(p\) and for each \(n \geq 7\), there exists a \(p\)-group \(G\) of order \(p^ n\) such that \(\text{Aut }G = \text{Aut}_ cG \cdot \text{Inn }G\), where \(\text{Aut}_ cG\) denotes the group of all central automorphisms of \(G\). Moreover, it is shown that the \(p\)-groups \(G\) of minimal order with \(\text{Aut }G = \text{Aut}_ cG \cdot \text{Inn }G\) have order \(p^ 6\) and nilpotency class 3. This answers a question of A. Caranti.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 627434
zbMATH Keywords: group of central automorphisms
zbMATH Keywords: \(p\)-groups
zbMATH Keywords: nilpotency class
author: Izabela Malinowska
MaRDI profile type: Publication
cites work: On a special class of \(p\)-groups
cites work: Endomorphisms of two-generated metabelian groups that induce the identity modulo the derived subgroup
cites work: Nilpotente Gruppen, deren sämtliche Normalteiler charakteristisch sind
cites work: Endliche Gruppen I
cites work: Some non-abelian p-groups with abelian automorphism groups
description: scientific article; zbMATH DE number 627434