Normal Subgroups Contained in Frattini Subgroups are Frattini Subgroups
Copyright policy )Normal Subgroups Contained in Frattini Subgroups are Frattini Subgroups
We prove that if N is a normal subgroup of the finite group G and if N ⊆ Φ ( G ) N \subseteq \Phi (G) , then there exists a finite group U such that N = Φ ( U ) N = \Phi (U) exactly. In particular, we see that the generalizations apparent in the conclusions of several recently stated theorems are illusory.
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Special subgroups (Frattini, Fitting, etc.), Finite nilpotent groups, \(p\)-groups, Subgroup theorems; subgroup growth, Series and lattices of subgroups
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Special subgroups (Frattini, Fitting, etc.), Finite nilpotent groups, \(p\)-groups, Subgroup theorems; subgroup growth, Series and lattices of subgroups
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