65th SAMS Congress
06-08 December 2022
Stellenbosch University
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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.