Problems on product of formations

 In formation theory, one of the interesting problems is the existence of a saturated formation which is a product of non-$p$-saturated formations. In this paper, we shall give an interesting example of saturated formation ${cal F}$ which is expressible by ${cal F}={cal M}{cal H},$ where ${cal M}$ and ${cal H}$ are both non-$p$-saturated formations for all $pin pi ({cal F}).$ We then prove that if the product formation ${cal F}={cal M}{cal H}$ of two formations ${cal M}$ and ${cal H}$ is a one-generated $w$-saturated formation with ${cal F}not ={cal H}$, then ${cal M}$ is also a $w$-saturated formation. By using this result, we shall answer two problems proposed by Skiba and Shemetkov. Received: 12 October 2001 / Revised version: 11 February 2002