Geodesic
A Question in the Theory of Totally Local Formations of Finite Groups
Algebra i logika, Tome 42 (2003) no. 6, pp. 727-736.

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It is proved that all proper totally local subformations of a non one-generated totally local formation $\mathfrak F$ of finite groups are one-generated iff $\mathfrak F$ coincides with a formation $\mathfrak S_\pi$ of all soluble $\pi$-groups, where $|\pi|=2$.
Keywords: totally local formation of finite groups
Mots-clés : soluble $\pi$-group. 
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V. G. Safonov. A Question in the Theory of Totally Local Formations of Finite Groups. Algebra i logika, Tome 42 (2003) no. 6, pp. 727-736. http://geodesic.mathdoc.fr/item/AL_2003_42_6_a5/

[1] A. N. Skiba, “Kharakterizatsiya konechnykh razreshimykh grupp zadannoi nilpotentnoi dliny”, Voprosy algebry, 3 (1987), 21–31 | MR | Zbl

[2] K. Doerk, “Zwei Klassen von Formationen endlicher auflösbarer Gruppen, deren Halbverband gesättigter Unterformationen genau ein maximales Element besitzt”, Arch. Math., 21:3 (1970), 240–244 | DOI | MR | Zbl

[3] T. Hawkes, “Skeletal classes of soluble groups”, Arch. Math., 22:6 (1971), 577–589 | DOI | MR | Zbl

[4] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978 | MR | Zbl

[5] L. A. Shemetkov, A. N. Skiba, Formatsii algebraicheskikh sistem, Nauka, M., 1989 | MR

[6] A. N. Skiba, Algebra formatsii, Belaruskaya navuka, Minsk, 1997 | MR | Zbl

[7] M. V. Selkin, Maksimalnye podgruppy v teorii klassov konechnykh grupp, Belaruskaya navuka, Minsk, 1997 | MR

[8] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992 | MR

[9] Guo Wenbin, The theory of classes of groups, Kluwer Academic Publ., Beijing, 2000 | MR

[10] Kh. Neiman, Mnogoobraziya grupp, Mir, M., 1969 | MR

[11] A. Yu. Olshanskii, “Razreshimye pochti-krossovy mnogoobraziya grupp”, Matem. sb., 85(129):1(5) (1979), 115–131 | MR

[12] A. N. Skiba, “O neodnoporozhdennykh $S$-zamknutykh lokalnykh formatsiyakh”, Arifmeticheskoe i podgruppovoe stroenie konechnykh grupp, Nauka i tekhnika, Minsk, 1986, 149–156 | MR

[13] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[14] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, 15-e izd., In-t matem. SO RAN, Novosibirsk, 2002 | MR