Journal of Mathematical Sciences

, Volume 166, Issue 5, pp 655–660 | Cite as

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

  • S. F. Kamornikov
  • L. A. Shemetkov


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 \( \mathfrak{N} \)-prefrattini subgroups and normalizers of Gaschütz systems, and investigate factorizations of the normalizer of a Gaschütz system.


Finite Group Maximal Subgroup Nilpotent Group System Normalizer Minimal Normal Subgroup 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Francisk Scorina Gomel State UniversityGomelBelarus

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