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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
Article

Abstract

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.

Keywords

Finite Group Maximal Subgroup Nilpotent Group System Normalizer Minimal Normal Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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