Automorphism groups of finite groupoids.
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.
scientific article; zbMATH DE number 5833778
scientific article