The exact bounds for the degree of commutativity of a \(p\)-group of maximal class. I
type: Item
instance of: scholarly article
title: The exact bounds for the degree of commutativity of a \(p\)-group of maximal class. I
zbMATH Open document ID: 1017.20013
DOI: 10.1016/S0021-8693(02)00157-6
author: A. Vera-López
author: M. A. García-Sánchez
author: J. M. Arregi
author: F. J. Vera-López
author: R. Esteban-Romero
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The goal of the series of papers of which the one under review is the first, which continue previous work on the subject by (some of) the authors, is to provide best possible estimates for the degree of commutativity of \(p\)-groups of maximal class. Recall that a group of order \(p^m\), where \(p\) is a prime and \(m\geq 4\), is said to be of maximal class if it has nilpotency class \(m-1\). The degree of commutativity of such a group is the greatest integer \(k\) such that \([G_i,G_j]\leq G_{i+j+k}\) for all \(i,j\geq 1\). Here \(G_i\) is the \(i\)-th term of the lower central series of \(G\), for \(i\geq 2\), whereas \(G_1=C_G(G_2/G_4)\). To obtain sharp estimates, the parameter space has to be divided into six regions; we refer to the paper for the details. Here, estimates for two of the regions are proved. In a forthcoming paper by Antonio Vera-López and A.~Jaikin-Zapirain, examples are constructed to show that these estimates are indeed sharp.
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 1868036
zbMATH Keywords: finite \(p\)-groups of maximal class
zbMATH Keywords: degree of commutativity
reviewed by: Andrea Caranti
describes a project that uses: GAP
MaRDI profile type: Publication
cites work: On a special class of \(p\)-groups
cites work: The exact lower bound for the degree of commutativity of a \(p\)-group of maximal class
cites work: Some bounds for the degree of commutativity of a p-group of maximal class, ii
cites work: Some bounds for the degree of commutativity of a p-group of maximal class, III
full work available at URL: s0021-8693(02)00157-6
OpenAlex ID: W2035434765
description: scientific article; zbMATH DE number 1868036