Geodesic
Local definitions of formations of finite groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 229-244

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A problem of constructing local definitions for formations of finite groups is discussed in the article. The author analyzes relations between local definitions of various types. A new proof of the existence of an $\omega$-composition satellite of an $\omega$-solubly saturated formation is obtained. It is proved that if a nonempty formation of finite groups is $\mathfrak X$-local by Förster, then it has an $\mathfrak X$-composition satellite. 
@article{FPM_2010_16_8_a11,
     author = {L. A. Shemetkov},
     title = {Local definitions of formations of finite groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {229--244},
     publisher = {mathdoc},
     volume = {16},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a11/}
}
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L. A. Shemetkov. Local definitions of formations of finite groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 229-244. http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a11/