On products of cyclic and abelian finite $p$-groups ($ p$ odd)

Abstract

For an odd prime p, it is shown that if G 1⁄4 AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p, then kðAÞB E G, where kðAÞ 1⁄4 hg 2 A j g k 1⁄4 1i.