Stellenbosch University
A new generalisation of Baer’s theorem
Adolfo Ballester-Bolinches,
Universitat de València
Sesuai Y. Madanha\(^*\), University of Pretoria
Tendai M. Mudziiri Shumba, Sobolev
Institute of Mathematics
Maria C. Pedraza-Aguilera, Universitat
Politècnica de València
Dedicated to the memory of Alexander Grant Robertson Stewart
SAMS Subject Classification Number: 15
In 1957, Reinhold Baer proved that if \(G\) is the product of two normal supersolvable subgroups and \(G'\) is nilpotent, then \(G\) is supersolvable. There has been several generalisations of this result. In this project the structure of finite groups \(G=AB\) which are a weakly mutually \(sn\)-permutable product of the subgroups \(A\) and \(B\), that is, such that \(A\) permutes with every subnormal subgroup of \(B\) containing \(A \cap B\) and \(B\) permutes with every subnormal subgroup of \(A\) containing \(A \cap B\), is studied. We generalise Baer’s theorem.
