Abstract
Let xe be a class of groups such that: (i) If G is in 3C, then every homomorphic image of G is in 3C. (ii) If G is finite and G/4(G) is in 3C, where +(G) is the Frattini subgroup of G, then G is in XC. Examples of such classes are the class of nilpotent groups and the class of supersolvable groups. Others can be found in a paper by Baer [1]. In this note a theorem of P. Hall on nilpotent groups is proved as a corollary to the following:
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