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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.
Completando i risultati esposti nella nota I dello stesso titolo ([1]) l'autore prova che se il gruppo finito G ha esattamente due classi di coniugazione di sottogruppi massimali, è G = PQ con P e Q rispettivamente p-sottogruppo di Sylow e q-sottogruppo di Sylow (p, q primi), P normale in G e Q ciclico. Inoltre Q opera irriducibilmente su .
Si apportano alcuni contributi diretti a provare una congettura relativa ai gruppi finiti dotati di due sole classi di coniugio di sottogruppi massimali.
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