FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 8, PAGES 229-244

Local definitions of formations of finite groups

L. A. Shemetkov

Abstract

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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 w-composition satellite of an w-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.

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