Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local definitions of formations of finite groups   A problem of constructing of 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 existence of an
$\omega$-composition satellite of an $\omega$-solubly saturated formation is
obtained. It is proved that if a non-empty formation of finite groups is
$\mathfrak X$-local by F\"{o}rster, then it has an $\mathfrak X$-composition
satellite.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys