Automorphisms of \(p\)-groups with cyclic commutator subgroup
type: Item
instance of: scholarly article
title: Automorphisms of \(p\)-groups with cyclic commutator subgroup
zbMATH Open document ID: 0824.20025
author: F. Menegazzo
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1994-12-14T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108311
review text: This paper contains a systematic study of the automorphism groups of finite, non abelian, 2-generated \(p\)-groups with cyclic commutator subgroup for odd primes \(p\). First the metacyclic groups are considered and then the non metacyclic groups are analysed in relation to the nontrivial direct factors of \(G/G'\) contained in \(C_ G(G')/G'\). For each case the orders of \(\text{Aut}(G)\), \(O_ p(\text{Aut}(G))\) and \(C_{\text{Aut}(G)}(G/\Phi(G))\) are computed. In many instances the effect of \(\text{Aut}(G)\) on two choosen generators of \(G\) is displayed.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 510100
zbMATH Keywords: automorphism groups
zbMATH Keywords: \(2\)-generated \(p\)-groups
zbMATH Keywords: cyclic commutator subgroup
zbMATH Keywords: metacyclic groups
zbMATH Keywords: orders
zbMATH Keywords: generators
reviewed by: Francisco Pérez-Monasor
MaRDI profile type: Publication
cites work: Endomorphisms of two-generated metabelian groups that induce the identity modulo the derived subgroup
cites work: On finite \(p\)-groups with cyclic commutator subgroup
cites work: On the Automorphism Group of a Finite p-Group with the Central Quotient Metacyclic
cites work: On p-groups with a cyclic commutator subgroup
description: scientific article; zbMATH DE number 510100