We obtain a necessary and sufficient criterion for the existence of an invariant complement to a nilpotent subgroup contained as a direct factor in one of the maximal subgroups of a given group; we also find a condition for the p-closure of a group, all proper subgroups of which are p-closed, expressed in terms of the degree of one of its nonlinear irreducible characters.
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S. A. Chunikhin, Subgroups of Finite Groups, Wolters-Noordhoff, Groningen, The Netherlands (1969).
W. Feit, Characters of Finite Groups, W. A. Benjamin, New York (1967).
A. V. Romanovskii, “Groups with Hall normal divisors,” in: Finite Groups [in Russian], Nauka i Tekhnika, Minsk (1966), pp. 98–115.
Translated from Matematicheskie Zametki, Vol. 16, No. 3, pp. 381–385, September, 1974.
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Romanovskii, A.V. Existence of Hall normal subgroups in finite groups. Mathematical Notes of the Academy of Sciences of the USSR 16, 817–819 (1974). https://doi.org/10.1007/BF01148126
- Normal Subgroup
- Finite Group
- Maximal Subgroup
- Irreducible Character
- Proper Subgroup