A note on amalgams
type: Item
instance of: scholarly article
title: A note on amalgams
zbMATH Open document ID: 0727.20020
author: Makoto Hayashi
published in: Hokkaido Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The author considers the typical amalgam situation. There is a group G generated by two finite subgroups \(P_ 1\), \(P_ 2\), \(P_ 1\cap P_ 2\) is a Sylow 2-subgroup of both \(P_ 1\) and \(P_ 2\), \(C_{P_ i}(O_ 2(P_ i))\subseteq O_ 2(P_ i)\), \(i=1,2\), and no nontrivial normal subgroup of G is contained in \(P_ 1\cap P_ 2\). Then as usual one introduces the coset graph. The main question is whether certain parameters of that graph are relevant for the structure of \(P_ 1\) and \(P_ 2\). For this he introduces a parameter b (which is not the same as the parameter b usually used in this area). Using this parameter he shows that it is possible to bound the number of noncentral chief factors within \(O_ 2(P_ i)\). It seems that the result is correct, but as the author introduces new objects in his proof without saying it is not possible to follow the proof. In fact the given examples are wrong as the parameters are miscalculated. Unfortunately the author uses these wrong values in his arguments.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 4200473
zbMATH Keywords: amalgam
zbMATH Keywords: Sylow 2-subgroup
zbMATH Keywords: coset graph
zbMATH Keywords: noncentral chief factors
reviewed by: Gernot Stroth
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381517490
OpenAlex ID: W1986222015
DOI: 10.14492/HOKMJ/1381517490
description: scientific article; zbMATH DE number 4200473