Abstract
It is proved that, if G is a finite group representable as a product of an abelian group A and a group B, then the center of B is contained in a solvable normal subgroup of G. The disposition of Op(Z(B)) in the upper p-series of a finite solvable group G having a factorization of this sort is determined. A corollary for locally finite groups is provided. Bibliography: 33 titles.
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