The Frattini subgroup of a direct product of groups
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Vlastimil Dlab, Vladimír Kořínek (1960)
Czechoslovak Mathematical Journal
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The intention of this paper is to provide an elementary proof of the following known results: Let G be a finite group of the form G = AB. If A is abelian and B has a nilpotent subgroup of index at most 2, then G is soluble.