Some finiteness questions about formations
Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 15-24

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In this paper we give negative answers to some open “finiteness questions” related to local and Baer-local formations of finite groups. Relevant examples are constructed explicitly. In particular, we describe a pair of local formations $(\mathfrak{F},\mathfrak{H})$ such that the set of all local formations that are contained in $\mathfrak{F}$ and not contained in $\mathfrak{H}$ has no minimal element.
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V. P. Burichenko. Some finiteness questions about formations. Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 15-24. http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a1/