On the existence of complements of residuals of finite group

JOURNAL OF ALGEBRA

卷:533

Article

Kamornikov, S. F.¹  Shemetkova, O. L.² 

[1] Francisk Scorina Gomel State Univ, Gomel, BELARUS

[2] Plekhanov Russian Univ Econ, Moscow, Russia

关键词: Finite group;    Formation;    Fitting formation;    Subnormal subgroup;    Residual;    Complement;   

DOI  :  10.1016/j.jalgebra.2019.04.039

来源: Elsevier

【 摘 要 】

L.A. Shemetkov's theorem on the complementability of the F-residual of a finite group is developed in the article. For an w-local Fitting formation F, it is proved that, if G is a finite group generated by subnormal subgroups A(1), ... , A(n), the subgroups A(1)(F), ... , A(n)F are w-soluble, and Sylow p-subgroups of A(1)(F), ... , A(n)F are abelian for every p is an element of w, then each wa-normalizer of G is an w-complement of G(F) in G. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free