Geodesic
On the normalizer of a~Gasch\"utz system of a~finite soluble group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 129-136

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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 $\mathfrak N$-prefrattini subgroups and normalizers of Gaschütz systems, and investigate factorizations of the normalizer of a Gaschütz system. 
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     author = {S. F. Kamornikov and L. A. Shemetkov},
     title = {On the normalizer of {a~Gasch\"utz} system of a~finite soluble group},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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S. F. Kamornikov; L. A. Shemetkov. On the normalizer of a~Gasch\"utz system of a~finite soluble group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 129-136. http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a6/