Abstract
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 $p\in \pi ({\cal F}).$ 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.
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Received: 12 October 2001 / Revised version: 11 February 2002
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Wenbin, G., Shum, K. Problems on product of formations. Manuscripta Math. 108, 205–215 (2002). https://doi.org/10.1007/s002290200274
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DOI: https://doi.org/10.1007/s002290200274