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RESEARCH ARTICLE

Hall operators on the set of formations of finite groups

Andrei P. Mekhovich^a, Nikolay N. Vorob'ev^b, Nikolay T. Vorob'ev<sup>b

a</sup> Polotsk State Agricultural Economic College, Oktyabrskaya street, 55, Polotsk, 211413, Belarus
^b Vitebsk State University of P. M. Masherov, Moscow Avenue, 33, Vitebsk, 210038, Belarus

Abstract: Let $\pi$ be a nonempty set of primes and let $\mathfrak F$ be a saturated formation of all finite soluble $\pi$-groups. It is constructed the saturated formation consisting of all finite $\pi$-soluble groups whose $\mathfrak F$-projectors contain a Hall $\pi$-subgroup.

Keywords: $\pi$-subgroup, $\pi$-soluble group, formation of finite groups, saturated formation, canonical satellite, $\mathfrak F$-projector.

MSC: 20D10

Received: 08.11.2009
Revised: 21.05.2010

Language: English

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