ON THE NORMALIZER OF A GASCHUETZ SYSTEM OF A FINITE SOLUBLE GROUP

摘要

The notion of a Gaschuetz 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 Gaschuetz systems are investigated. In particular, we calculate the number of Gaschuetz systems in a finite soluble group and prove their conjugacy, obtain a connection between N-prefrattini subgroups and normalizers of Gaschutz systems, and investigate factorizations of the normalizer of a Gaschuetz system.