Infinite groups with Sylow permutable subgroups.
Let \(G\) be a periodic group. A subgroup \(H\) of \(G\) is said to be `\(S\)-permutable' if \(HP=PH\) for each Sylow subgroup \(P\) of \(G\). It is known that \(S\)-permutability is not a transitive relation, and a `PST-group' is a periodic group in which \(S\)-permutability is transitive. In the paper under review, the authors extend a result of \textit{R. K. Agrawal} [Proc. Am. Math. Soc. 47, 77-83 (1975; Zbl 0299.20014)] on finite PST-groups to the case of radical hyperfinite groups (recall here that a group is `hyperfinite' if it has an ascending normal series with finite factors). Moreover, the relationship between PST-groups and groups in which all ascendant subgroups are \(S\)-permutable is investigated.
scientific article; zbMATH DE number 5805948