On the normal index of maximal subgroups of a finite group. (English) Zbl 0686.20016
This paper is a new one in a series of papers dealing with the study of the structure of a finite group in terms of the normal index of maximal subgroups in the sense of W. E. Deskins [Proc. Symp. Pure Math. 1, 100-104 (1959; Zbl 0096.248)]. This series started with a paper of the first author [Ill. J. Math. 19, 173-178 (1975; Zbl 0303.20014)]. Other references may be found in the present authors’ paper [Pac. J. Math. 132, 143-149 (1988; Zbl 0649.20019)].
In the paper under review, the influence of the normal indices of certain classes of maximal subgroups of a given group on the structure of the group is studied. As a consequence, various characterizations of nilpotent, supersolvable and other classes of finite groups are given in these terms.
In the paper under review, the influence of the normal indices of certain classes of maximal subgroups of a given group on the structure of the group is studied. As a consequence, various characterizations of nilpotent, supersolvable and other classes of finite groups are given in these terms.
Reviewer: M.Deaconescu
MSC:
20D25 | Special subgroups (Frattini, Fitting, etc.) |
20E28 | Maximal subgroups |
20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |