Automorphism groups of finite groupoids.
type: Item
instance of: scholarly article
title: Automorphism groups of finite groupoids.
zbMATH Open document ID: 1217.20039
author: David Hobby
author: Donald Silberger
author: Sylvia Silberger
published in: Algebra Universalis
publication date: 2011-01-07T00:00:00Z
review text: The authors describe the content very well in their abstract: ``Given a finite set \(M\) of size \(n\) and a subgroup \(G\) of \(\text{Symm}(M)\), \(G\) is `pertinent' iff it is the automorphism group of some groupoid \(\langle M;*\rangle\). We examine when subgroups of \(\text{Symm}(M)\) are and are not pertinent. For instance, \(A_n\), the alternating group on \(M\), is not pertinent for \(n>4\).'' The techniques of proof are combinatorial (as for example the proof of the identity in Theorem 1.1); Section 3 of the article relates pertinence to transitivity, while section 4 speculates on different ways to generalize the concept of pertinence.
reviewed by: Marian Deaconescu
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 08A35
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 5833778
zbMATH Keywords: finite groupoids
zbMATH Keywords: automorphism groups
MaRDI profile type: Publication
full work available at URL: s00012-010-0093-0
OpenAlex ID: W2085082955
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DOI: 10.1007/S00012-010-0093-0
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description: scientific article; zbMATH DE number 5833778