Minimal covers of \(S_ n\) by abelian subgroups and maximal subsets of pairwise noncommuting elements. II
The author follows up the investigations in his earlier paper [Part I, ibid. 49, No.2, 294-307 (1988; Zbl 0666.20012)] with new conclusions about the minimum cardinality \(\beta_ n\) of a cover of the symmetric group \(S_ n\) by abelian subgroups, and the maximum cardinality \(\alpha_ n\) of a set of pairwise non-commuting elements of \(S_ n\). He now shows that \(\alpha_ n\neq \beta_ n\) for \(n=8\), 13 and all \(n\geq 15\), and that the ratio \(\beta_ n/\alpha_ n\) has no limit and takes infinitely many values arbitrary close to 1.
scientific article; zbMATH DE number 4177358