On mutually \(m\)-permutable product of smooth groups. (English) Zbl 1300.20029
A group \(G\) is said to be a mutually \(m\)-permutable product of two subgroups \(H\) and \(K\) if \(G=HK\) and every maximal subgroup of \(H\) permutes with \(K\) and every maximal subgroup of \(K\) permutes with \(H\). In the current paper, the authors investigate the structure of a finite group that is a mutually \(m\)-permutable product of two subgroups under the assumption that its maximal subgroups are totally smooth.
Reviewer: Marius Tărnăuceanu (Iaşi)
MSC:
20D40 | Products of subgroups of abstract finite groups |
20D30 | Series and lattices of subgroups |
20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
20E28 | Maximal subgroups |