A note on bounds of the \(p\)-length of a \(p\)-soluble group. (English) Zbl 1506.20019
Summary: Suppose that the finite group \(G=AB\) is a mutually permutable product of two \(p\)-soluble subgroups \(A\) and \(B\). By using the Wielandt lenghts of Sylow \(p\)-subgroups of \(A\) and \(B\), we present a new bound of the \(p\)-length of \(G\). Some known results are improved.
MSC:
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20D40 | Products of subgroups of abstract finite groups |
References:
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