FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 8, PAGES 129-136

**On the normalizer of a Gaschütz system of a finite
soluble group**

S. F. Kamornikov

L. A. Shemetkov

Abstract

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The notion of a Gaschütz system of a finite soluble
group was introduced by S. F. Kamornikov in 2008 (this
is a set of complements of crowns of pairwise nonisomorphic
non-Frattini factors of a chief series of the group).
In the present paper, properties of Gaschütz systems are
investigated.
In particular, we calculate the number of Gaschütz systems in
a finite soluble group and prove their conjugacy, obtain
a connection between $\$\; \backslash mathfrak\; N\; \$$-prefrattini subgroups and
normalizers of Gaschütz systems, and investigate factorizations
of the normalizer of a Gaschütz system.

Location: http://mech.math.msu.su/~fpm/eng/k08/k088/k08807h.htm

Last modified: October 18, 2009