Geodesic
On a~problem of Sz\'ep
Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 467-495

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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 $O_p(Z(B))$ 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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     author = {L. S. Kazarin},
     title = {On a~problem of {Sz\'ep}},
     journal = {Izvestiya. Mathematics },
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     number = {3},
     year = {1987},
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L. S. Kazarin. On a~problem of Sz\'ep. Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 467-495. http://geodesic.mathdoc.fr/item/IM2_1987_28_3_a2/