Darji, U. B.; Mitchell, J. D. Highly transitive subgroups of the symmetric group on the natural numbers. (English) Zbl 1139.20001 Colloq. Math. 112, No. 1, 163-173 (2008). The main algebraic result of this paper states that given any nonidentity element \(\alpha\in S_\mathbb{N}\), there exists a cycle \(\beta\in S_\mathbb{N}\) with support \(\mathbb{N}\) such that the subgroup generated by \(\alpha\) and \(\beta\) is highly transitive. The Baire category method is used to prove that for certain types of permutations \(\alpha\) there are many such possibilities for \(\beta\). Reviewer: Dimitru Buşneag (Craiova) Cited in 3 Documents MSC: 20B22 Multiply transitive infinite groups 20B35 Subgroups of symmetric groups 54H11 Topological groups (topological aspects) Keywords:highly transitive permutation groups; symmetric group on countable set PDFBibTeX XMLCite \textit{U. B. Darji} and \textit{J. D. Mitchell}, Colloq. Math. 112, No. 1, 163--173 (2008; Zbl 1139.20001) Full Text: DOI