On BNA-normality and solvability of finite groups. (English) Zbl 1368.20010
Summary: Let \(G\) be a finite group. A subgroup \(H\) of \(G\) is called a BNA-subgroup if either \(H^x=H\) or \(x\in \langle H, H^x\rangle\) for all \(x\in G\). In this paper, some interesting properties of BNA-subgroups are given and, as applications, the structure of the finite groups in which all minimal subgroups are BNA-subgroups have been characterized.
MSC:
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D30 | Series and lattices of subgroups |
| 20D25 | Special subgroups (Frattini, Fitting, etc.) |
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
References:
| [1] | pp. |
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