Geodesic
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/

[1] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978

[2] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin, 1993 | MR

[3] Gaschütz W., “Zur Theorie der endlichen auflösbaren Gruppen”, Math. Zeit., 80 (1963), 300–305 | DOI | MR | Zbl

[4] V. D. Mazurov, E. I. Khukhro (red.), Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 12-e izd., In-t mat. SO RAN, Novosibirsk, 1992 http://math.nsc.ru/alglog/17kt.pdf

[5] Burichenko V. P., “On a problem of Gaschütz”, J. Algebra, 372 (2012), 428–458 | DOI | MR | Zbl

[6] Shemetkov L. A., Skiba A. N., Formatsii algebraicheskikh sistem, Nauka, M., 1989

[7] Safonov V. G., “O suschestvovanii minimalnoi $\tau$-zamknutoi totalno nasyschennoi ne $\mathfrak{H}$-formatsii”, Trudy In-ta matematiki NAN Belarusi, 16:1 (2008), 67–72 | Zbl

[8] Skiba A. N., Shemetkov L. A., “O minimalnom kompozitsionnom ekrane kompozitsionnoi formatsii”, Voprosy algebry, 7, Universitetskoe, Minsk, 1992, 39–43 | MR