Some characterizations of \(\pi\)-solvable and supersolvable groups using \(\theta\)-pairs. (English) Zbl 0997.20024
Summary: For a finite group \(G\), \(D_p(G)\) is a generalization of the Frattini subgroup of \(G\). We obtain some results on \(\pi\)-solvable and supersolvable groups with the help of \(D_p(G)\) using \(\theta\)-pairs.
MSC:
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20D25 | Special subgroups (Frattini, Fitting, etc.) |
